Quantum roots for Kac-Moody root systems and finiteness properties of the Kac-Moody affine Bruhat order - École Centrale de Lyon Access content directly
Preprints, Working Papers, ... Year : 2024

Quantum roots for Kac-Moody root systems and finiteness properties of the Kac-Moody affine Bruhat order

Abstract

Let $G$ be a split Kac-Moody group over a local field. In their study of the Iwahori-Hecke algebra of $G$, A.Braverman, D. Kazhdan and M. Patnaik defined a partial order - called the affine Bruhat order - on the extended affine Weyl semi-group $W^+$ of $G$. In this paper, we study finiteness questions for covers and co-covers of $W^+$, generalizing results of A. Welch. In particular we prove that the intervals for this order are finite. Our results rely on the finiteness of the set of quantum roots of arbitrary Kac-Moody root systems, which we prove. We also obtain a classification of quantum roots.
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Dates and versions

hal-04579365 , version 1 (17-05-2024)

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  • HAL Id : hal-04579365 , version 1

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Auguste Hebert, Paul Philippe. Quantum roots for Kac-Moody root systems and finiteness properties of the Kac-Moody affine Bruhat order. 2024. ⟨hal-04579365⟩
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