We consider the Iwahori–Hecke algebra associated to an almost split Kac–Moody group (affine or not) over a nonarchimedean local field . It has a canonical double-coset basis indexed by a sub-semigroup of the affine Weyl group . The multiplication is given by structure constants : . A conjecture, by Braverman, Kazhdan, Patnaik, Gaussent and the authors, tells that is a polynomial, with coefficients in , in the parameters of over . We prove this conjecture when and are spherical or, more generally, when they are said to be generic: this includes all cases of if is of affine or strictly hyperbolic type. In the split affine case (where , ) we get a universal Iwahori–Hecke algebra with the same basis over a polynomial ring ; it specializes to when one sets .
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Keywords: Building, Hecke algebra, Kac–Moody group, masure, local field.
@article{ALCO_2021__4_3_465_0, author = {Bardy-Panse, Nicole and Rousseau, Guy}, title = {On structure constants of {Iwahori{\textendash}Hecke} algebras for {Kac{\textendash}Moody} groups}, journal = {Algebraic Combinatorics}, pages = {465--490}, publisher = {MathOA foundation}, volume = {4}, number = {3}, year = {2021}, doi = {10.5802/alco.163}, language = {en}, url = {http://www.numdam.org/articles/10.5802/alco.163/} }
TY - JOUR AU - Bardy-Panse, Nicole AU - Rousseau, Guy TI - On structure constants of Iwahori–Hecke algebras for Kac–Moody groups JO - Algebraic Combinatorics PY - 2021 SP - 465 EP - 490 VL - 4 IS - 3 PB - MathOA foundation UR - http://www.numdam.org/articles/10.5802/alco.163/ DO - 10.5802/alco.163 LA - en ID - ALCO_2021__4_3_465_0 ER -
%0 Journal Article %A Bardy-Panse, Nicole %A Rousseau, Guy %T On structure constants of Iwahori–Hecke algebras for Kac–Moody groups %J Algebraic Combinatorics %D 2021 %P 465-490 %V 4 %N 3 %I MathOA foundation %U http://www.numdam.org/articles/10.5802/alco.163/ %R 10.5802/alco.163 %G en %F ALCO_2021__4_3_465_0
Bardy-Panse, Nicole; Rousseau, Guy. On structure constants of Iwahori–Hecke algebras for Kac–Moody groups. Algebraic Combinatorics, Volume 4 (2021) no. 3, pp. 465-490. doi : 10.5802/alco.163. http://www.numdam.org/articles/10.5802/alco.163/
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