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- W1586177581 abstract "This thesis considers three topics related to therepresentations of Coxeter systems, their Hecke algebras, andrelated groups. The first topic concerns the construction ofgeneralized involution models, as defined by Bump and Ginzburg. Wecompute the automorphism groups of all complex reflection groupsG(r, p, n) and using this information, we classify precisely whichcomplex reflection groups have generalized involution models. Thesecond topic concerns the set of unipotent characters Uch(W)which Lusztig has attached to each finite, irreducible Coxetersystem (W, S). We describe a precise sense in which the irreduciblemultiplicities of a certain W-representation can be used to definea function which serves naturally as a heuristic definition of theFrobenius-Schur indicator on Uch(W). The formula we obtain for thisindicator extends prior work of Casselman, Kottwitz, Lusztig, andVogan addressing the case in which W is a Weyl group. Finally, westudy a certain module of the Hecke algebra of a Coxeter system (W,S), spanned by the set of twisted involutions in W. Lusztig hasshown that this module has two distinguished bases, and that thetransition matrix between these bases defines interesting analogsof the much-studied Kazhdan-Lusztig polynomials of (W, S). We proveseveral positivity properties related to these polynomials foruniversal Coxeter systems, using combinatorial techniques, and forfinite Coxeter systems, using computationalmethods." @default.
- W1586177581 created "2016-06-24" @default.
- W1586177581 creator A5066022731 @default.
- W1586177581 date "2013-01-01" @default.
- W1586177581 modified "2023-10-18" @default.
- W1586177581 title "Coxeter systems, multiplicity free representations, and twisted Kazhdan-Lusztig Theory" @default.
- W1586177581 hasPublicationYear "2013" @default.
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