Let $\mathfrak{G}$ be a split reductive group, $\mathbb{k}$ be a field and ${\varpi }$ be an indeterminate. In order to study $\mathfrak{G}(\mathbb{k}[{\varpi },{\varpi }^{-1}])$ and $\mathfrak{G}(\mathbb{k}({\varpi }))$, one can make them act on their twin building $\mathscr{I}=\mathscr{I}_\oplus \times \mathscr{I}_{\ominus }$, where $\mathscr{I}_{\oplus }$ and $\mathscr{I}_{\ominus }$ are related via a “codistance”.
Masures are generalizations of Bruhat–Tits buildings adapted to the study of Kac–Moody groups over valued fields. Motivated by the work of Dinakar Muthiah on Kazhdan–Lusztig polynomials associated with Kac–Moody groups, we study the action of $\mathfrak{G}(\mathbb{k}[{\varpi },{\varpi }^{-1}])$ and $\mathfrak{G}(\mathbb{k}({\varpi }))$ on their “twin masure”, when $\mathfrak{G}$ is a split Kac–Moody group instead of a reductive group.
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Keywords: Kac–Moody groups, masures, twinning
Bardy-Panse, Nicole 1; Hébert, Auguste 1; Rousseau, Guy 1
CC-BY 4.0
@article{ART_2025__2_3_281_0,
author = {Bardy-Panse, Nicole and H\'ebert, Auguste and Rousseau, Guy},
title = {Twin masures associated with {Kac{\textendash}Moody} groups over {Laurent} polynomials},
journal = {Annals of Representation Theory},
pages = {281--353},
publisher = {The Publishers of ART},
volume = {2},
number = {3},
year = {2025},
doi = {10.5802/art.25},
language = {en},
url = {https://art.centre-mersenne.org/articles/10.5802/art.25/}
}
TY - JOUR AU - Bardy-Panse, Nicole AU - Hébert, Auguste AU - Rousseau, Guy TI - Twin masures associated with Kac–Moody groups over Laurent polynomials JO - Annals of Representation Theory PY - 2025 SP - 281 EP - 353 VL - 2 IS - 3 PB - The Publishers of ART UR - https://art.centre-mersenne.org/articles/10.5802/art.25/ DO - 10.5802/art.25 LA - en ID - ART_2025__2_3_281_0 ER -
%0 Journal Article %A Bardy-Panse, Nicole %A Hébert, Auguste %A Rousseau, Guy %T Twin masures associated with Kac–Moody groups over Laurent polynomials %J Annals of Representation Theory %D 2025 %P 281-353 %V 2 %N 3 %I The Publishers of ART %U https://art.centre-mersenne.org/articles/10.5802/art.25/ %R 10.5802/art.25 %G en %F ART_2025__2_3_281_0
Bardy-Panse, Nicole; Hébert, Auguste; Rousseau, Guy. Twin masures associated with Kac–Moody groups over Laurent polynomials. Annals of Representation Theory, Volume 2 (2025) no. 3, pp. 281-353. doi : 10.5802/art.25. https://art.centre-mersenne.org/articles/10.5802/art.25/
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