2013/06/21 by Sean Rostami, Rostami, Sean
Mathematics · #20C08 #20F55 #22E50 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #Finite Group Theory Research #Representation Theory (math.RT) #math.RT #msc:20C08 #msc:20F55 #msc:22E50
paper · pdf · doi:10.48550/arxiv.1306.5255
31 pages total w/ 1.5 spacing and 6 picture pages, referee response incorporated (to appear in Trans. Amer. Math. Soc.), updated acknowledgements and bibliography; should be final version
openalex publication_date 2013/06/21 · arxiv created 2014/11/11 · arxiv updated 2014/11/12 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28
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.