Register to reply

Reducibility tensor product representation

Share this thread:
Yoran91
#1
May26-13, 02:46 AM
P: 37
Hello everyone,

Say I have two irreducible representations [itex]\rho[/itex] and [itex]\pi[/itex] of a group [itex]G[/itex] on vector spaces [itex]V[/itex] and [itex]W[/itex]. Then I construct a tensor product representation
[itex]\rho \otimes \pi : G\to \mathrm{GL}\left(V_1 \otimes V_2\right)[/itex]
by
[itex]\left[\rho \otimes \pi \right] (g) v\otimes w = \rho (g) v \otimes \pi (g) w [/itex].

I now wish to know whether or not this representation is reducible or irreducible. If it cannot be determined, then I wish to know what further conditions imply reducibility or irreducibility. However, I have not been able to find an answer to this anywhere. Can anyone provide some insight?

Thanks for any help.
Phys.Org News Partner Mathematics news on Phys.org
Researcher figures out how sharks manage to act like math geniuses
Math journal puts Rauzy fractcal image on the cover
Heat distributions help researchers to understand curved space

Register to reply

Related Discussions
Irreducible representation of tensor field High Energy, Nuclear, Particle Physics 3
Symmetric vector to tensor representation? Differential Geometry 1
Tensor products of representation - Weyl spinors and 4vectors Quantum Physics 10
Double inner product of derivative of a 2nd order tensor with another 2ndorder tensor Linear & Abstract Algebra 3
Is there an infinite product representation of e^(z) Calculus 13