Séminaire SPACE Tours
Cellularity of the lowest two-sided ideal of an affine Hecke algebraJérémie Guilhot (LMPT)
Friday 27 September 2013 11:00 - Tours - Salle 1180 (Bât E2)
Résumé :
This talk is concerned with affine Weyl groups and their associated affine Hecke algebras. A special feature of affine Weyl groups is that there is a distinguished Kazhdan-Lusztig cell, the so-called lowest two-sided cell, which contains, roughly speaking, most of the elements of the group. Attached to this cell is the lowest two-sided ideal of the Hecke algebra which comes naturally equipped with the Kazhdan-Lusztig basis. The aim of this talk is to show that this ideal is affine cellular. Throughout the talk, we will focus on type affine A_2. In this case, we will explicitely describe the cellular basis and show that the basis elements have a nice decomposition when expressed in the Kazhdan-Lusztig basis. More precisely, we will provide a combinatorial description of this decomposition in term of number of paths.
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