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- W4300695919 abstract "Let W be an Iwahori-Weyl group of a connected reductive group G over a non-archimedean local field. I prove that if w is an element of W that does not act on the corresponding apartment of G by a translation then one can apply to w a sequence of conjugations by simple reflections, each of which is length-preserving, resulting in an element w' for which there exists a simple reflection s such that l(sw's)>l(w'). Even for affine Weyl groups, a special case of Iwahori-Weyl groups and also an important subclass of Coxeter groups, this is a new fact about conjugacy classes. Further, there are implications for Iwahori-Hecke algebras H of G: one can use this fact to give dimension bounds on the length-filtration of the center Z(H), which can in turn be used to prove that suitable linearly-independent subsets of Z(H) are a basis." @default.
- W4300695919 created "2022-10-04" @default.
- W4300695919 creator A5025938213 @default.
- W4300695919 date "2013-06-21" @default.
- W4300695919 modified "2023-10-09" @default.
- W4300695919 title "Conjugacy classes of non-translations in affine Weyl groups and applications to Hecke algebras" @default.
- W4300695919 doi "https://doi.org/10.48550/arxiv.1306.5255" @default.
- W4300695919 hasPublicationYear "2013" @default.
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