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Multiplicity-free Representations of Algebraic Groups

Martin W. LiebeckGary M. SeitzDonna Testerman

出版	American Mathematical Society, 2024
主題	Mathematics / Group Theory
ISBN	14704775489781470477547
URL	http://books.google.com.hk/books?id=TJu80AEACAAJ&hl=&source=gbs_api

註釋

"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