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arXiv · 1810.06851

Representation theory of disconnected reductive groups

P. Achar·W. Hardesty·S. Riche
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Abstract

We study three fundamental topics in the representation theory of disconnected algebraic groups whose identity component is reductive: (i) the classification of irreducible representations; (ii) the existence and properties of Weyl and dual Weyl modules; and (iii) the decomposition map relating representations in characteristic $0$ and those in characteristic $p$ (for groups defined over discrete valuation rings). For each of these topics, we obtain natural generalizations of the well-known results for connected reductive groups.

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BibTeXRIS

P. Achar, W. Hardesty, S. Riche. 2020-09-08. Representation theory of disconnected reductive groups. https://arxiv.org/abs/1810.06851

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