All Questions
Tagged with reductive-groups unitary-representations
7 questions
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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 ...
- 11
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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 ...
3
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40
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Generating $K$-types of a $(\mathfrak g,K)$-module for $K$ disconnected
Let $G$ be a real reductive Lie group, let $K$ be a maximal compact subgroup of $G$, and let $V$ be a $(\mathfrak g,K)$-module. For $\sigma\in\widehat{K}$ we denote the $\sigma$-isotypic component of $...
- 741
2
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1
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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 ...
- 951
5
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1
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Supercuspidal with Iwahori fixed vector
Let $F$ be a local field. Is there a reference for the following fact:
No supercuspidal representation of $GL_2(F)$ has an Iwahori-fixed vector?
I have a proof, by I'd prefer a reference, because ...
- 11.2k
3
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1
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611
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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/...
- 11.2k
5
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2
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523
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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, ...
- 11.2k