Multiplicity-free representations of algebraic groups
Keywords: Algebraic group, representation theory, multiplicity-free representation, irreducible subgroup
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| Format: | UnknownFormat |
| Sprache: | eng |
| Veröffentlicht: |
Providence, RI
American Mathematical Society
February 2024
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| Schriftenreihe: | Memoirs of the American Mathematical Society
volume 294, number 1466 (February 2024) |
| Schlagworte: |
Representations of groups
> Linear algebraic groups
> Group theory and generalizations -- Linear algebraic groups and related topics -- Representation theory
> Group theory and generalizations -- Linear algebraic groups and related topics -- Linear algebraic groups over the reals, the complexes, the quaternions
> Reduktive Gruppe
> Einfacher Modul
> Multiplizität
> Darstellungstheorie
> Dominantes Gewicht
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| Online Zugang: | Inhaltsverzeichnis zbMATH |
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Tag hinzufügen | Zusammenfassung: | Keywords: Algebraic group, representation theory, multiplicity-free representation, irreducible subgroup "Let K be an algebraically closed field of characteristic zero, and let G be a connected reductive algebraic group over K. We address the problem of classifying triples (G,H, V ), where H is a proper connected subgroup of G, and V is a finitedimensional irreducible G-module such that the restriction of V to H is multiplicityfree - that is, each of its composition factors appears with multiplicity 1. A great deal of classical work, going back to Dynkin, Howe, Kac, Stembridge, Weyl and others, and also more recent work of the authors, can be set in this context. In this paper we determine all such triples in the case where H and G are both simple algebraic groups of type A, and H is embedded irreducibly in G. While there are a number of interesting familes of such triples (G,H, V ), the possibilities for the highest weights of the representations defining the embeddings H < G and G < GL(V ) are very restricted. For example, apart from two exceptional cases, both weights can only have support on at most two fundamental weights; and in many of the examples, one or other of the weights corresponds to the alternating or symmetric square of the natural module for either G or H"-- |
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| Beschreibung: | "February 2024, volume 294, number 1466 (third of 5 numbers)" Literaturverzeichnis: Seite 267-268 |
| Beschreibung: | vii, 268 Seiten |
| ISBN: | 9781470469054 978-1-4704-6905-4 |