On the stable moment graph of an affine Kac--Moody algebra
Martina Lanini
TL;DR
This paper introduces the stable moment graph for affine Kac-Moody algebras, providing a categorical perspective on Lusztig's stabilization of affine Kazhdan-Lusztig polynomials using sheaves on moment graphs.
Contribution
It presents a novel categorical framework for the stable moment graph of affine Kac-Moody algebras, extending Lusztig's stabilization results.
Findings
Categorical version of Lusztig's stabilization property
Construction of the stable moment graph for Kac-Moody algebras
Connection between sheaves on moment graphs and affine Kazhdan-Lusztig polynomials
Abstract
In 1980 Lusztig proved a stabilisation property of the affine Kazhdan-Lusztig polynomials. In this paper we give a categorical version of such a result using the theory of sheaves on moment graphs. This leads us to associate with any Kac-Moody algebra its stable moment graph.
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