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arXiv · 2504.14911

Lusztig sheaves, decomposition rule and restriction rule

Yixin Lan
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Abstract

In this article, we realize the subquotient based modules of certain tensor products or restricted modules via Lusztig's perverse sheaves on multi-framed quivers, and provide a construction of their canonical bases. As an application, we prove that the decomposition and restriction coefficients of symmetric Kac-Moody algebras equal to the dimensions of top Borel-Moore homology groups for certain locally closed subsets of Nakajima's quiver varieties.

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Yixin Lan. 2025-04-21. Lusztig sheaves, decomposition rule and restriction rule. https://arxiv.org/abs/2504.14911

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