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arXiv · 2504.11403

Counting irreducible representations of general linear groups and unitary groups

Qiutong Wang
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Abstract

Let $G$ be a general linear group over $\BR$, $\BC$, or $\BH$, or a real unitary group. In this paper, we precisely describe the number of isomorphism classes of irreducible Casselman-Wallach representations of $G$ with a given infinitesimal character and a given associated variety, expressed in terms of certain combinatorial data called painted Young diagrams and assigned Young diagrams.

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Qiutong Wang. 2025-04-15. Counting irreducible representations of general linear groups and unitary groups. https://arxiv.org/abs/2504.11403

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