Skip to main content

All Questions

Filter by
Sorted by
Tagged with
5 votes
2 answers
523 views

Steinberg reps of reductive groups over local fields vs finite fields

Let $G$ be a reductive group over a non-archimedean field $F$ with reisdue field $f$. Edit: The statements only make sense modulo tensoring by one-dimensional representations. Are the unitary, ...
Marc Palm's user avatar
  • 11.2k
3 votes
1 answer
611 views

How to translate the representation theory of semisimple to reductive groups?

I am aware of the following question: Definitions of Reductive and Semisimple Groups So let me phrase a precise question: Is there a standard technique by which one can translate the unitary/...
Marc Palm's user avatar
  • 11.2k
2 votes
1 answer
271 views

Discrete decomposability of unitary representation

[INTRODUCTION] Let $G$ be a non-compact simple Lie group, and $G'$ a reductive subgroup of $G$. Suppose that $\pi$ is a non-trivial (hence, infinite dimensional) irreducible unitary representation of ...
Hebe's user avatar
  • 951
1 vote
0 answers
58 views

Linear algebraic group, absolute root system, computing roots

Let $G(F)$ be a reductive linear algebraic group, where $F$ is a local field. Let $T(F)$ be a maximal anisotropic torus of $G$ that splits over a quadratic extension of $F$. Is there an efficient ...
user536406's user avatar
0 votes
0 answers
134 views

Tempered representations and unramified principal series

For $V$ a tempered representation of connected reductive group over a local field of characteristic zero. I want to show that for an Iwahori subgroup $B$, the set of fixed points $V^B\neq 0$, thereby ...
InteresetingStuff's user avatar