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
'Moral victories' might spare you from losing again
Fair cake cutting gets its own algorithm
Effort to model Facebook yields key to famous math problem (and a prize)

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