What is Representations: Definition and 216 Discussions

Representations is an interdisciplinary journal in the humanities published quarterly by the University of California Press. The journal was established in 1983 and is the founding publication of the New Historicism movement of the 1980s. It covers topics including literary, historical, and cultural studies. The founding editorial board was chaired by Stephen Greenblatt and Svetlana Alpers. Representations frequently publishes thematic special issues, for example, the 2007 issue on the legacies of American Orientalism, the 2006 issue on cross-cultural mimesis, and the 2005 issue on political and intellectual redress.

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  1. M

    Circuit schematics: Equivalent Representations of circuits

    Attached is a schematic of interest. Assume same voltage source and capacitance for each capacitor in each circuit. Correct me if I'm wrong, it appears all circuitry comprises two basic types of connection: series and parallel. I'm trying to figure out an approach to determining whether a...
  2. K

    Van de Waals fluid in Free energy, Enthelpy representations

    Compute the coefficient of expansion α in terms of P and V... Homework Statement Compute the coefficient of expansion α in terms of P and V for an ideal Van der Waals gas Homework Equations (p+a/v^2)(v-b)=RT The Attempt at a Solution Is this as simple as solving for a? How...
  3. micromass

    Geometry Lie Groups, Lie Algebras, and Representations by Hall

    Author: Brian Hall Title: Lie Groups, Lie Algebras, and Representations: An Elementary Introduction Amazon link https://www.amazon.com/dp/1441923136/?tag=pfamazon01-20 Level: Grad Table of Contents: General Theory Matrix Lie Groups Definition of a Matrix Lie Group Counterexamples...
  4. C

    State space representations for different system configurations

    Homework Statement Homework Equations This is the problem that I am trying to solve. The Attempt at a Solution https://docs.google.com/file/d/0B0Wxm870SWTNV0xjdmVRc09TTm8/edit The approach of solving this problem is to first convert the two systems' state space...
  5. H

    What do the graphical representations of waves actually represent?

    I know how waves work, by the oscillation of particles along there mean position..fine I know how a simple oscillatory motion can be described by a sinusoidal wave , and what is its physical significance...okay but what I don't understand when waves (say a transverse) wave is represented by a...
  6. V

    Irreducible representations of the Lorentz group

    I'm having some difficulty understanding the representation theory of the Lorentz group. While it's a fundamentally mathematical question, mathematicians and physicists use very different language for representation theory. I think a particle physicist will be more likely than a mathematician to...
  7. G

    Finding Normal Modes of Oscillation with matrix representations

    Homework Statement Two equal masses (m) are constrained to move without friction, one on the positive x-axis and one on the positive y axis. They are attached to two identical springs (force constant k) whose other ends are attached to the origin. In addition, the two masses are connected to...
  8. W

    Kernels, and Representations of Diff. Forms.

    Hi, All: I need some help with some "technology" on differential forms, please: 1)Im trying to understand how the hyperplane field Tx\Sigma< TpM on M=\Sigma x S1 , where \Sigma is a surface, is defined as the kernel of the form dθ (the top form on S1). I know that...
  9. E

    Encyclopedia of Gamma Matrix Representations?

    Hello, I was just curious if anyone knew of a single place with a list of many different gamma matrix representations, I haven't been able to find what I want by just searching google. In particular, I'm looking for a representation of the 5+1 dimensional Clifford algera. In other dimensions...
  10. N

    Find the matrix representations of the Differentiation Map in the Basis

    Homework Statement Show that B = {x2 −1,2x2 +x−3,3x2 +x} is a basis for P2(R). Show that the differentiation map D : P2(R) → P2(R) is a linear transformation. Finally, find the following matrix representations of D: DSt←St, DSt←B and DB←B. Homework Equations The Attempt at a...
  11. D

    Can there be multiple power series representations for a function?

    I guess this is a simple question. Say I am tasked with finding the Taylor series for a given function. Well say that the function is analytic and so we know there's a taylor series representation for it. Am I gauranteed that this representation is the only power series representation for it...
  12. C

    Representations of the Lorentz group

    Can anyone recommend some litterature on representations of the Lorentz group. I'm reading about the dirac equation and there the spinor representation is used, but I would very much like to get a deeper understanding on what is going on.
  13. M

    Functional Analysis or group representations?

    I have to choose a total of 12 modules for my 3rd year. I've everything decided except four of them. I want to eventually do research either General Relativity, quantum mechanics, string theory, something like that. I'm torn between Group Representations, with one of Practical numerical...
  14. S

    Is this result trivial? (improper integral representations of real functions))

    I'm a college Sophomore majoring in math and over the summer I've been playing around with improper integrals, specifically integrals with limits at infinity because they've always fascinated me. The highest calculus course I've taken is Calc II, so I might be missing something here. Anyways...
  15. P

    Lorentz invariant theory, irreducible representations

    "In a Lorentz invariant theory in d dimensions a state forms an irreducible representation under the subgroups of SO(1,d-1) that leaves its momentum invariant." I want to understand that statement. I don't see how I should interpret a state as representation of a group. I have learned that...
  16. Z

    Series representations of function

    I have been reading about the legendre polynomials and how their completeness allows you to write any function as a sum of them. I have seen that used in electrostatics for the multipole expansion, which I guess is pretty nice, but here's the deal: It seems that I am to learn more and more...
  17. A

    Complex and Real Representations, their differences by decomposition

    Homework Statement Decompose \mathbb{C}^{5}, the 5 dimensional complex Euclidean space) into invariant subspaces irreducible with respect to the group C_{5} \cong \mathbb{Z}_{5} of cyclic permutations of the basis vectors e_{1} through e_{5}. Hint: The group is Abelian, so all the irreps...
  18. ArcanaNoir

    Group representations, interesting aspects?

    I am writing an undergraduate "thesis" on group representations (no original work, basically a glorified research paper). I was wondering if anyone could suggest interesting aspects that might be worth writing about in my paper. I have only just begun to explore the topic, and I see that it...
  19. K

    Equivalence of definitions for regular representations

    There seem to be two definitions for a regular representation of a group, with respect to a field k. In particular, one definition is that the regular representation is just left multiplication on the group algebra kG, while the other is defined on the set of all functions f: G \to k . I do not...
  20. quasar987

    Exploring SO(3) Representations: Trivial or Complex?

    Is it true that SO(3) has no complex 2-dimensional representation (except the trivial one...)? How to see this? If it is nontrivial, can someone provide a source? Is there such a thing as a classification of all the linear representations of SO(n)? Thanks
  21. E

    Charge Conjugation and Internal Symmetry Representations

    Hi All, I am trying to work through a QFT problem for independent study and I can't quite get my head around it. It is 5.16 from Tom Bank's book (http://www.nucleares.unam.mx/~Alberto/apuntes/banks.pdf) which goes as follows: "Show that charge conjugation symmetry implies that the...
  22. R

    Direct product of faithful representations into direct sum

    Direct product of two irreducible representations of a finite group can be decomposed into a direct sum of irreducible representations. So, starting from a single faithful irreducible representation, is it possible generate every other irreducible representation by successively taking direct...
  23. Math Amateur

    Representations of Groups - S3

    I am reading Dummit and Foote Ch 18, trying to understand the basics of Representation Theory. I need help with clarifying Example 3 on page 844 in the particular case of S_3 . (see the attahment and see page 844 - example 3) Giving the case for S_3 in the example we have the...
  24. Math Amateur

    Representations of the cyclic group of order n

    I am reading James and Liebeck's book on Representations and Characters of Groups. Exercise 1 of Chapter 3 reads as follows: Let G be the cyclic group of order m, say G = < a : a^m = 1 >. Suppose that A \in GL(n \mathbb{C} ) , and define \rho : G \rightarrow GL(n \mathbb{C} ) by...
  25. O

    Representations of lorentz group and transformations IN DETAIL

    From Peskin and Schroeder: The finite-dimentional representations of the rotation group correspond precisely to the allowed values for the angular momentum: integers or half integers. From the Lorentz commutation relations: \left[J^{\mu \nu},J^{\rho \sigma}\right]=i \left(g^{\nu \rho}J^{\mu...
  26. T

    On spinor representations and SL(2,C)

    Hi guys! I still have problem clearing once and for all my doubt on the spinor representation. Sorry, but i just cannot catch it. 1) ----- Take a left handed spinor, \chi_L. Now, i know it transforms according to the Lorentz group, but why do i have to take the \Lambda_L matrices belonging...
  27. O

    Representations of subgroups; character tables

    I'm having some trouble with a concept in group theory. I'm reading Howard Georgi's book on Lie Algebra, this is from the 1st chapter. Really sorry to have to use a picture but I don't know how to TeX a table: There's a couple things I don't quite understand but mainly, I don't see how he...
  28. O

    Exploring the Equivalence of FG-Modules and Group Representations

    There is a Theorem that says FG-Modules are equivalent to group representations: "(1) If \rho is a representation of G over F and V = F^{n}, then V becomes an FG-Module if we define multiplication vg by: vg = v(g\rho), for all v in V, g in G. (2) If V is an FG-Module and B a basis of V...
  29. R

    State space representations in LTI systems

    I just started my first graduate level controls class this semester, and it looks like my professors notes aren't going to be quite enough. Can anybody recommend a good book with lots of state space representation examples, or if not a book, a website would do fine as well. Thanks for any help.
  30. S

    Representations of Symmetry Operators

    For spin 1/2 particles, I know how to write the representations of the symmetry operators for instance T=i\sigma^{y}K (time reversal operator) C_{3}=exp(i(\pi/3)\sigma^{z}) (three fold rotation symmetry) etc. My question is how do we generalize this to, let's say, a basis of four...
  31. R

    Group representations on tensor basis.

    I am a physicist, so my apologies if haven't framed the question in the proper mathematical sense. Matrices are used as group representations. Matrices act on vectors. So in physics we use matrices to transform vectors and also to denote the symmetries of the vector space. v_i = Sum M_ij...
  32. S

    Vector Representations of Quantum States

    I happen to be studying the basics of quantum mechanics at the moment and have made acquaintance with the vector representation of quantum states, in particular the two states of electron spin. For this question let's just say the spin can be up or down. The state of the spin is...
  33. A

    Two Kraus representations: How to check if they're the same TPCPM?

    Hi According to the Kraus representation theorem, a map \mathcal{E}: \text{End}(\mathcal{H}_A) \rightarrow \text{End}(\mathcal{H}_B) is a trace-preserving completely positive map if and only if it can be written in an operator sum representation \mathcal{E}: \rho \mapsto \sum_k A_k \rho...
  34. A

    Deriving info from reducible representations

    Heres the reducible representation made by counting the number of bonds left unchanged by each symmetry operation of water: http://img808.imageshack.us/img808/704/red0.png and here's the irreducible representations extracted from it: http://imageshack.us/m/695/3829/red01l.png in the book...
  35. Y

    Representations of the Lorentz Group

    This is something I feel I should know by now, but I've always been very confused about. Specifically, how does one determine what each representation of the Lorentz group corresponds to? I mean, I know that the (1/2,0) and the (0,1/2) representations correspond to right and left handed spinors...
  36. K

    How Do You Solve This Moving Average Representation Problem in Time Series?

    Hi everyone! I really need your help if you are good in time series. I have a problem on moving average representations. I attach the problem description; also, I attach my attempt to solve it. Cannot go any further. Please please help me. Thank you!
  37. C

    Gamma matrices and projection operator question on different representations

    Typically I understand that projection operators are defined as P_-=\frac{1}{2}(1-\gamma^5) P_+=\frac{1}{2}(1+\gamma^5) where typically also the fifth gamma matrices are defined as \gamma^5=i\gamma^0\gamma^1\gamma^2\gamma^3 and.. as we choose different representations the projection...
  38. G

    Representations in group theory

    The group theory course I'm taking is driving me crazy. It's a mandatory class in my undergraduate physics studies but it's all very alien and very abstract to me and my books scarcely give any examples when introducing new concepts. It's just so much harder than calculus or physics courses...
  39. C

    Query regarding representations and Clebsch-Gordan series

    Hello all, I'm stuck on understanding part of a discussion of representations and Clebsch-Gordan series in the book 'Groups, representations and Physics' by H F Jones. I'd be grateful to anyone who can help me out. For starters, this discussion is in the SU(2) case. I don't know how to...
  40. G

    Representations and irreducible subrepresentations

    I don't know how to do the following homework: Let Gbe a finite group and let \rho : G \rightarrow GL(E)be a finite-dimensional faithful complex representation, i.e. ker \rho = 1. For any irreducible complex representation \piof G, show that there exists k \geq 1 such that \pi is an...
  41. D

    Space time distortion grid representations

    Hi, I'm a newbie here, i joined just now purely to ask this question that's been on my mind recently. Now i apologise if this question is fundamentally wrong (which it probably is), but I'm only the average person with an amateur interest in physics :P So don't laugh. Firstly, as you know, we...
  42. C

    Exploring Irreducible Representations of Clifford Algebra

    I'm doing a course which assumes knowledge of Group Theory - unfortunately I don't have very much. Can someone please explain this statement to me (particularly the bits in bold): "there is only one non-trivial irreducible representation of the Cliford algebra, up to conjugacy" FYI The...
  43. C

    Adjoint representations and Lie Algebras

    I have a very superficial understanding of this subject so apologies in advance for what's probably a stupid question. Can someone please explain to me why if we have a Lie Group, G with elements g, the adjoint representation of something, eg g^{-1} A_\mu g takes values in the Lie Algebra of G...
  44. R

    How Do You Determine Irreducible Representations for Group Transformations?

    I don't understand how to find the irreducible representations of a group. Under transformation U: (T')^{ijk}=U^{il}U^{jm}U^{kn}T^{lmn} But suppose (M')^{ijk}=(T')^{ijk}+\pi (T')^{jik} Then (M')^{ijk}=U^{il}U^{jm}U^{kn}T^{lmn} +\pi U^{jl}U^{im}U^{kn}T^{lmn}=U^{il}U^{jm}U^{kn}(T^{lmn}+\pi...
  45. antibrane

    On Finding Lie Algebra Representations

    What I am trying to do is start with a Dynkin diagram for a semi-simple Lie algebra, and construct the generators of the algebra in matrix form. To do this with su(3) I found the root vectors and wrote out the commutation relations in the Cartan-Weyl basis. This gave me the structure constants...
  46. M

    Tensor products of representations

    I'm a mathematician, and I have trouble understanding the physics notation. I'm glad if someone could help me out. Here's my question: Let g be a Lie algebra and r_1: g -> End(V_1), r_2: g -> End(V_2) be two representations. Then there is a representation r3:=r_1 \otimes r_2: g -> End...
  47. T

    Mobius: Representations of SU(2,1)=U(1,1)

    I'm studying the representations of SU(2,1) [or U(1,1)], and since they are non-compact, their representations are necessarily infinite dimensional. I have a couple questions. In the literature, they say the algebra satisfied by the three generators, T_1, T_2, T_3 is [T_1,\,T_2]=-i T_3...
  48. M

    Representations of a noncompact group

    Hi all, It's a well-known result that any finite or compact group G admits a finite-dimensional, unitary representation. A standard proof of this claim involves defining a new inner product of two vectors by averaging the inner products of the images of the vectors under each element of the...
  49. C

    Irreducible representations and elementary particles

    Hi, I had a question about irreducible representations and elementary particles... Namely, I've been told by teachers and read in a few texts that particles ARE irreducible representations, and I have never been able to wrap my mind around what that means. Please keep in mind that I am no...
  50. L

    Show that representations of the angular momentum

    Show that representations of the angular momentum algebra [J_i, J_j ] = \epsilon_{ijk}J_k act on finite-dimensional vector spaces, V_j , of dimension 2j + 1, where j = 0, 1/2, 1, \dots This sounds incredibly easy but what is the question actually asking me to do?
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