Generalized Induction of Kazhdan-Lusztig cells
Copyright policy )Generalized Induction of Kazhdan-Lusztig cells
Following Lusztig, we consider a Coxeter group W together with a weight function. Geck showed that the Kazhdan-Lusztig cells of W are compatible with parabolic subgroups. In this paper, we generalize this argument to some subsets of W which may not be parabolic subgroups. We obtain two applications: we show that under specific technical conditions on the parameters, the cells of certain parabolic subgroups of W are cells in the whole group, and we decompose the affine Weyl group of type G into left and two-sided cells for a whole class of weight functions.
Representation theory for linear algebraic groups, weight functions, unions of left cells, [MATH] Mathematics [math], Coxeter groups, parabolic subgroups, generalized induction, Hecke algebras and their representations, Reflection and Coxeter groups (group-theoretic aspects), affine Weyl groups, FOS: Mathematics, Kazhdan-Lusztig cells, Representation Theory (math.RT), Mathematics - Representation Theory
Representation theory for linear algebraic groups, weight functions, unions of left cells, [MATH] Mathematics [math], Coxeter groups, parabolic subgroups, generalized induction, Hecke algebras and their representations, Reflection and Coxeter groups (group-theoretic aspects), affine Weyl groups, FOS: Mathematics, Kazhdan-Lusztig cells, Representation Theory (math.RT), Mathematics - Representation Theory
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