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Linear representations of algebras and groups, Lie theory, associative algebras, multilinear algebra.

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 \ …
Joseph Hundley's user avatar
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 …
Joseph Hundley's user avatar
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 $ …
Joseph Hundley's user avatar
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 $ …
Joseph Hundley's user avatar