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Results tagged with rt.representation-theory
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user 6355
Linear representations of algebras and groups, Lie theory, associative algebras, multilinear algebra.
7
votes
Accepted
Is there a generalization of Burnside's theorem for compact Lie groups?
The answer is yes--use the Weyl character formula, for example.
See: Patrick X. Gallagher, Zeros of group characters. Math. Z. Volume 87 (1965), Number 3.
- 1,639
2
votes
How to calculate symmetric tensor products of SO(10) representations?
I think you can probably prove this by induction using Littelmann paths. Since the (16 dimensional) spin rep is minuscule, you can at least figure out the tensor powers by adding up weights of the fo …
- 1,639
5
votes
0
answers
249
views
generators for Hecke algebra quotients
What are generators for the kernel of the (k,r)-quotient of the Hecke algebras of type A? Are just the two projections onto the reps. corresponding to Young digarams with 1-row of length r-k+1 and th …
- 1,639
3
votes
3
answers
189
views
Simultaneous "Monomialization" of a set of operators.
We all know that a set of commuting diagonalizable matrices can be simultaneously put in diagonal form. My general question is:
Under what conditions can a set of (diagonalizable) matrices be sim …
- 1,639
2
votes
0
answers
89
views
explicit matrices for Weil ($p^2$ dimensional) representation of $Sp(4,\mathbb{F}_p)$, $p>3$
I am looking for more-or-less explicit matrices for the $p^2$ dimensional Weil representation of $Sp(4,\mathbb{F}_p)$, suitable for computer implementation. Ideally, I would like the images of the ge …
- 1,639
6
votes
Accepted
schur weyl duality for real orthogonal groups and relation to hyperoctahedral groups
The $O(n)$ version of Schur-Weyl duality involves Brauer algebras, the structure of which was not worked out completely until the 1980s by Hans Wenzl (Ann. of Math. (2) 128 (1988), no. 1, 173–193.) S …
- 1,639
5
votes
Why is there such a close resemblance between the unitary representation theory of the Viras...
I think it is not a coincidence, although the only relationship I can think of is a bit distant. Roughly, it goes: From positive energy representations of affine Kac-Moody algebras one gets certain v …
- 1,639
6
votes
0
answers
133
views
Do purification and equivariantization commute?
Suppose that we have an action of a group $G$ on a (quasi-)Hopf algebra $H$, so that we can construct $H\rtimes G$ as in Majid's Cross Products by Braided Groups and Bosonization. It is known that $R …
- 1,639