Geodesic
Representation Theory of Disconnected Reductive Groups
Documenta mathematica, Tome 25 (2020), pp. 2149-2177
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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 of mixed characteristic). For each of these topics, we obtain natural generalizations of the well-known results for connected reductive groups.
DOI : 10.4171/dm/796
Classification : 17B10, 20C15, 20G05
Mots-clés : disconnected reductive groups, Clifford theory 
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     author = {William D. Hardesty and Simon Riche and Pramod N. Achar},
     title = {Representation {Theory} of {Disconnected} {Reductive} {Groups}},
     journal = {Documenta mathematica},
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     doi = {10.4171/dm/796},
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William D. Hardesty; Simon Riche; Pramod N. Achar. Representation Theory of Disconnected Reductive Groups. Documenta mathematica, Tome 25 (2020), pp. 2149-2177. doi: 10.4171/dm/796

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