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. S

    Deriving equations from fourier series representations

    Say you have the coefficients a_k of a Fourier series representation of some function x(t). You can easily then give x(t) as $$x(t) = \sum_{k = -\infty}^{\infty} a_k e^{i k \omega_0 t}$$ But this doesn't do much good in telling you what the actual function looks like. For example, if we have...
  2. S

    Irreducible Representations and Class

    So I'm studying molecules and symmetry and I was wondering if there was a intuitive way of understanding why there are as many irreducible representations as there are classes. I keep getting lost in the math of the characters.
  3. N

    Matrix representations of linear transformations

    Homework Statement Let g(x)=3+x and T(f(x))=f'(x)g(x)+2f(x), and U(a+bx+cx2)=(a+b,c,a-b). So T:P2(R)-->P2(R) and U:P2(R)-->R3. And let B and y be the standard ordered bases for P2 and R3 respectively. Compute the matrix representation of U (denoted [U]yB) and T ([T]yB) and their...
  4. haushofer

    SUSY gauge theories and representations

    Hi, I'm currently reading "Supersymmetry demystifed" by Patrick Labelle, chapter 10, about SUSY non-Abelian gauge theories. We have a Lagrangian with SU(N)-gauge fields, and gaugino's. What puzzles me are the following claims of Labelle about the representations. In the...
  5. J

    Wondering about operators and matrix representations?

    Hi, this isn't a homework question per se (it's the summer hols, I'm between semesters) but it's something that I never really got during the QM module I just did. I found myself blindly calculating exam & homework problems, and just feel like this is some stuff I should get cleared up...
  6. W

    Any good reference on construction of irreducible representations of SU(N)?

    how to construct an irreducible representation of SU(3)?
  7. L

    Induced representations of the wavefunction

    Hi, hopefully this is the right board to ask this on. I'm currently reading Groups, representations and Physics by Jones, and trying to get my head around induced transformations of the wavefunction. The problem is I seem to understand nearly all of what he's saying except the crucial part I...
  8. N

    Anomaly of representations in SU(N)

    Homework Statement The problem is the following: Compute the ratio of the anomaly of the N to that of the N(N-1)/2 representations in SU(n) Homework Equations Georgi claims that you can find the anomaly, A(R) of the [1] representation of SU(n) by calculating the anomaly of SU(3) (subgroup of...
  9. K

    Representations of finite groups

    I'm just having a little trouble getting my head around how representation theory works. Say for example we are working with the dihedral group D8. Then the degrees of irreducible representations over C are 1,1,1,1,2. So there are 4 (non-equivalent) irreduible representations of degree 1...
  10. tom.stoer

    Representations of the Poincare group

    Hello, in relativistic quantum field theories all particles are members of (unitary) representations of the Poincare group. For massive particles m² > 0 one gets the usual scalar / spinor / vector representations with spin J = 0, 1/2, 1, 3/2, ... and dim. rep. = 2J+1. For massless particles...
  11. M

    Different representations of SU3 and resultant multiplets

    I have a very basic query about multiplets. In the SU(3) approach strongly interacting particles, quarks and hadrons are the basis vectors of irreducible representations of SU(3). Now, quarks and hadrons are definite properties with define eigenvalues of hypercharge and isospin: to put it...
  12. T

    Point symmetry group matrix representations

    Is there any book or source avaliable that clearly shows the point symmetry operation with matrix representations?
  13. N

    Representations and change of basis

    Hi guys 1) We are looking at a Hamiltonian H. I make a rotation in Hilbert space by the transformation {\cal H} = \mathbf a^\dagger\mathsf H \mathbf a = \mathbf a^\dagger \mathsf U\mathsf U^\dagger\mathsf H \mathsf U\mathsf U^\dagger\mathbf a = \mathbf b^\dagger...
  14. V

    A simple question on representations and tensor products

    I have question, can someone please check whether my answer is correct or not: 1)Let \pi_i be representations of a group G on vector spaces Vi, i = 1, 2. Give a formula for the tensor product representation \pi_1 \otimes \pi_2 on V_1 \otimes V_2 Answer: \pi_1 V_1 \otimes \pi_2 V_2 2)Check...
  15. R

    Reducing infinite representations (groups)

    Hi, I am trying to work through some problems I have found in preparation for a test. I am running out of time, and getting somewhat confused, however... Homework Statement a) Show that every irreducible representation of SO(2) has the form \Gamma\ \left( \begin{array}{ccc} cos(\theta) &...
  16. V

    Exploring Representations: Understanding Fundamental and Unitary Representations

    These are probably a bit stupid, so I hope you don't mind me asking them... 1)what is a fundamental representation? 2)what is a unitary representation? (Is it just the identity matrix?) 3)What is meant by the 'orthogonal complement' in the following context? "If W\subset{V} is an...
  17. R

    Irreducible representations of translations

    I read somewhere that the irreducible representations of Lie groups were countable. But what about translations? Isn't each momentum value its own irreducible singlet, and there are a continuum of momentum values? For example take e^{ipx} . If you translate it, it doesn't mix with anything...
  18. T

    Particles as representations of groups

    Hello everyone. I need someone to explain a concept to me. I'm confused about how a type of particle can be a representation of a lie group. For example, I read that particles with half-integer spin j are a representation of the group SU(2), or that particles with charge q are a...
  19. M

    Classification of the representations of the Lorentz algebra

    The complexified Lie algebra of the Lorentz group can be written as a direct sum of two commuting complexified Lie algebras of SU(2). It is being said, that this enables us to classify the irreducible representations of the Lorentz algebra with two half-integers (m,n). But can someone...
  20. C

    How to get from representations to finite or infinitesimal transformations?

    Hi all. I have here a reference with a representation of the Lie algebra of my symmetry group in terms the fields in my Lagrangian. In order to calculate Noether currents, I would like to use this representation to derive formulae for the infinitesimal forms of the symmetry transformations...
  21. R

    Representations of Lorentz group

    I'm reading the wiki article on Representation theory of the Lorentz group and they seem to make a distinction between these two reps: (1/2,1/2) and (1/2,0) + (0,1/2) I did some checks and it seems that these two are the same. Am I wrong or is the wiki article wrong (won't be the...
  22. W

    Characteristic classes of finite group representations

    I know zero about the characteristic classes of finite group representations and would appreciate a reference. specifically, if I have a faithful representations of a finite group,G, in O(n) what can I say about the induced map on cohomology, P*:H*(BO(n))-> H*(BG) ? I am mostly interested in...
  23. A

    Irreducible Representations of so(4,C)

    Does anyone know how to classify the finite-dimensional irreducible representations of so(4,C)? Can they all be built from irreducible reps of sl(2,C) given the fact that so(4,C) \cong sl(2,C) \times sl(2,C). Thanks!
  24. N

    Massless representations of the Poincare group

    Never mind, I answered my own question...
  25. O

    Representations of the Fundamental Group

    This is not important, but it's been bugging me for a while. I'm struggling to see how the locally constant sheaves of vector spaces on X give rise to representations of the fundamental group of X. The approach I've been thinking of is the following. Given a locally constant sheaf F on X...
  26. B

    Groups and representations

    I have a few questions: 1) The tensor product of two matrices is define by A \otimes B =\left( {\begin{array}{cc} a_{11}B & a_{12}B \\ a_{21}B & a_{22}B \\ \end{array} } \right) for the 2x2 case with obvious generalisation to higher dimensions. The tensor product of two...
  27. R

    Are there any such symbolic representations of Pi or ex?

    Howdy folks. The Gelfond-Schneider Constant 221/2 is transcendental. Of my understanding, transcendental numbers are a special case of irrational numbers in the sense of how they may or may not be derrived. This being the case, how is it that many infinite series are stated with such...
  28. R

    Understanding SU(N) Representations and Subgroups

    The fundamental representation of SU(N) has a basic form that allows you to deduce that there is a SU(N-1) subgroup. For example, in SU(3), the generators T_{1}, T_{2}, T_{3} form an SU(2) subgroup. I'm reading a book right now that goes into the adjoint representation of SU(N) to show that...
  29. T

    Representations of algebras?

    1. Can an algebra have an infinite number of non isomorphic representations? 2. Can an algebra have two different representations where one is irreducible and the other is reducible? 3. In general, is it easy to come up with a representation of an algebra? If so then is there a preference for...
  30. P

    Products of representations

    Hi, I have a problem. Consider the representation of SU(2) which maps every U \in SU(2) into itself, i.e. U \mapsto U , and the vector space is given by \mathbb{C}^{2} with the basis vectors e_{1} = (1,0) and e_{2} = (0,1) How do I show that the tensor product (Kronecker) of the...
  31. H

    Linear representations

    Let H be a separable Hilbert space. What are the continuous linear representations of S^1 on H? I read in an article this is defined as in the finite-dim case. Why is this so? Thanks.
  32. O

    Terminology issue regarding modules and representations

    Homework Statement Given a field F, FS4 is a group algebra... we have a representation X that maps FS4 to 3x3 matrices over (presumably) F. Let V denote the FS4 module corresponding to X... do stuff. My question is, what the heck is V supposed to be? I assumed that V is F3, but that...
  33. B

    Representations of the lorentz group

    I'm very very very confused and extremely thick. If \Lambda_i is some element of the Lorentz group and \Lambda_j is another, different element of the group then under multiplication... \Lambda_i \Lambda_j is also an element of the Lorentz group, say \Lambda_i \Lambda_j...
  34. J

    Understanding Group Representations in Group Theory

    Hey guys, I'm pretty new to group theory at the moment, what's the best way of understanding a 'representation' of a group? Thanks
  35. Q_Goest

    Are semantic representations innate?

    In his book, "Representation and Reality" Hilary Putnam writes about Chomsky: So what do you think? Are there ‘semantic representations’ in the mind that are innate and universal? Or would you go along with Putnam? If they are not innate/universal, then how do you think meaning gets...
  36. P

    Why Irreducibel Representations?

    Hallo, I would like to know why physicists are always seeking for irreducible representation of a given group. I know that a reducible one is decomposable into irreducible representations (under special circumstances), but what is the physical motivation that irreducible reps are fundamental...
  37. A

    Completeness of irreducible representations

    "Completeness" of irreducible representations Hi, For a finite group of order n each irreducible representation consists of n matrices [D(g)], one for each element in the group. For a given row and column (e.g. i,j) you can form an n-dimensional vector by taking the ij element of D(g) for each...
  38. M

    Parametric Equations for Circle and Spiral Curves

    I was wondering if someone could give me an overview of what they are and how to get them. Thanks
  39. J

    What are the v_j vectors in Cahn's representation of the Lie algebra of SO(3)?

    Hi all, I asked this on the Quantum Physics board but didn't get a response. I'm reading Cahn's book on semi-simple lie algebras and their representations. http://www-physics.lbl.gov/~rncahn/book.html In chapter 1, he attempts to build a (2j+1)-dimensional representation T of the Lie...
  40. J

    What are weight spaces and how do they relate to the representation of SU(2)?

    I'm taking a course on Lie groups and am reading alongisde Cahn's semi-simple lie algebras and their representations. On page 4 he starts to construct a representation T of the Lie group corresponding to SU(2) acting on a linear space V, by defining the action of T_z and T_+ on a vector v_j...
  41. M

    How to Make Direct Product of Representations for the Lorentz Group?

    [SOLVED] Lorentz Representations I am reading about the Lorentz group on Schweber. My problem is the following: I don't really understand how to make the direct product of Representations for this Group. I know that we need only 2 mubers since the invarints of the gropu are 2. I know the...
  42. V

    Plotting Phasor representations of functions

    Homework Statement Plot the following for x = 0 to 8: This is part of a larger engineering problem, but I am stuck here, I have no idea how to plot a phasor. The original function is: y(x,\,t)\,=\,2\,cos\left(\frac{\pi}{6}\,t\,-\,\frac{\pi}{4}\,x\right) Homework Equations...
  43. C

    Several problems on series representations, residue theorem

    First question pertains to the Residue Theorem We are to use this theorem to evaluate the integral over the given path... There is one problem from this section that I am stuck on. An example in the book evaluates \int_{\Gamma} e^{1/z} dz for \Gamma any closed path not passing through...
  44. B

    M-Curves: Representations & Properties of C^oo Manifolds

    Let q and q' be sufficiently close points on C^oo manifold M. Then is it true that any C^oo curve c:[a,b]-->M where c(a)=q, c(q)=q' can be represented as c(t)=exp_{q}(u(t)v(t)) where u:[a,b]-->R,v:[a,b]-->TM_{q} and ||v||=1? My question comes from Chapter 9 corollary 16 and 17 of Spivak vol1...
  45. P

    Spin/ angular momentum, representations of SO(3), SU(2)

    Homework Statement I'm trying to understand why particles have both spin and angular momentum in terms of group theory. As I understand it orbital angular momentum comes from the normal generators SO(3) which are intuitively infintesimal rotations so d/d(theta) etc. Also spin comes from...
  46. L

    Semi-Simple Lie Algebra Representations

    I'm trying to prove that any representation of a semisimple Lie algebra can be uniquely decomposed into irreducible representations. I have seen some sketches of proofs that show that any representation \phi of a semisimple Lie algebra which acts on a finite-dimensional complex vector space...
  47. J

    Parametric Representations of Circles and Ellipses

    Sketch and represent parametrically the following: (a) \mid z+a+\iota b\mid =r \ \mbox { clockwise}\\ , (b) ellipse 4(x-1)^2 + 9(y+2)^2 =36 \ . Taking (a) first \mid z + a + \iota b \mid = r \mbox{- is the distance between the complex numbers }\ z=x+\iota y \ \mbox{ and } \ a + \iota b \...
  48. A

    Representations of SU(2) are equivalent to their duals

    Hi. I am having trouble proving that the irreducible representations of SU(2) are equivalent to their dual representations. The reps I am looking at are the spaces of homogenous polynomials in 2 complex variables of degree 2j (where j is 0, 1/2, 1,...). If f is such a polynomial the action of...
  49. D

    Field operators in canonically transformed representations of the CCRs

    Here's a question about inequivalent representations of the CCRs... For a given Hilbert space representation, what is it that determines which set of field operators \phi(x), or \phi(f) if we want to get rigorous a la Wightman, gives us THE field operators for that representation. For example...
  50. C

    Simple graphical representations: what language should I use?

    I'm currently learning Python, but right now I'm interested in animating the motion of things like projecticles, bouncing balls, etc. What language is good for doing stuff like this? And are there any add ons for Python that allow this?
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