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Multiplicity-free representations of algebraic groups / Martin W. Liebeck, Gary M. Seitz, Donna M. Testerman

By: Contributor(s): Resource type: Ressourcentyp: BuchBookLanguage: English Series: American Mathematical Society. Memoirs of the American Mathematical Society ; volume 294, number 1466 (February 2024)Publisher: Providence, RI : American Mathematical Society, February 2024Description: vii, 268 SeitenISBN:
  • 9781470469054
Subject(s): Additional physical formats: 9781470477547 | Erscheint auch als: Multiplicity-Free Representations of Algebraic Groups. Online-Ausgabe 1st ed. Providence : American Mathematical Society, 2024. 1 online resource (282 pages) | Erscheint auch als: Multiplicity-free representations of algebraic groups. Online-Ausgabe Providence, RI : American Mathematical Society, 2024. 1 Online-Ressource (vii, 268 Seiten)DDC classification:
  • 512/.2 23/eng20240809
MSC: MSC: 20G05 | 20G20 | 20G05RVK: RVK: SI 130LOC classification:
  • QA176
Summary: Keywords: Algebraic group, representation theory, multiplicity-free representation, irreducible subgroupSummary: "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"--PPN: PPN: 1887322930
Holdings
Item type Home library Shelving location Call number Status
Institutsbestand Fachbibliothek Mathematik Bibliothek / frei aufgestellt Z 57 c-294.2024,1466 Nicht ausleihbar
Total holds: 0
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