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Results tagged with rt.representation-theory
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user 21252
Linear representations of algebras and groups, Lie theory, associative algebras, multilinear algebra.
5
votes
Accepted
Restriction of irreducible representations
If Archimedean local fields are ok, then the simplest example probably occurs with $G=GL(2, \mathbb R)$ and $K=SO(2, \mathbb R).$ The irreducible representations of $K$ are in bijection with the inte …
- 590
5
votes
Accepted
Generic representations of $GL(n,F)$
No. At least I think not.
I assume that $Ind_U^G \chi$ means the space of all functions $f:G\to \mathbb C$ which satisfy (1) $f(ug) = \chi(u) f(g)$ and (2) there is an open compact subgroup $K$ of $ …
- 590
4
votes
1
answer
256
views
Reference request: normalization of intertwining operators for GL(2, C)
Take $F$ a local field and $\chi_1, \chi_2$ two characters, write $M(\chi_1, \chi_2)$ for the standard intertwining integral
$$M(\chi_1. \chi_2).f(g) := \int_{F} f\left( \begin{pmatrix} 0&-1\\ 1& 0 \ …
- 590
1
vote
Generic representations of $GL(n,F)$
It seems to me that the universal property that you want for an "$L$-minimal" representation is precisely the universal property of the direct sum. In other words, the direct sum of the elements of $ …
- 590