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Results tagged with rt.representation-theory
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user 979
Linear representations of algebras and groups, Lie theory, associative algebras, multilinear algebra.
3
votes
How is the longest increasing subsequence a matrix integral?
There is a roundabout way of putting this.
A discrete analogue of random matrix spectra is random partitions (=Young diagrams). There clearly is a 'gadget' relating random permutations with random You …
- 1,765
12
votes
2
answers
2k
views
A decomposition of the "spin representation" of SL(2)
Let us take an N-dimensional (N odd) irreducible representation V of SL(2,R).
It is known that (e.g., Lie groups and Lie algebras III by Vinberg and Onischik, 1994 p. 94) in V there is an invariant …
- 1,765
5
votes
Accepted
Asymptotic character theory of unitary groups via shifted Schur functions
Yes, they probably mean https://arxiv.org/abs/q-alg/9709011
There, they consider the Jack generalization of the problem, but if you set $\theta=1$, then you get the theory of characters of the unitary …
- 1,765
18
votes
0
answers
466
views
Quasi-classical limit of representation theory
I am looking for a good reference on a general phenomenon of quasi-classical limit in representation theory, which relates "large" representations to measures on (co-adjoint orbits of) the associated …
- 1,765
6
votes
Accepted
Formula for $U(N)$ integration wanted
To expand on my comments, this paper https://arxiv.org/pdf/hep-th/9209083v2.pdf by Shatashvili deals
with ``correlation functions'' of Haar unitary matrices of the form
$$
\int_{U(N)}^{} d\mu(U) e_{}^ …
- 1,765