The parity of Lusztig's restriction functor and Green's formula for a quiver with automorphism

2024/06/05 by Jiepeng Fang, Yixing Lan, Fang, Jiepeng +3 · 1 citation
Mathematics · #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology #Commutative Algebra and Its Applications

paper · pdf · doi:10.48550/arxiv.2406.03238

Abstract

In [8], Fang-Lan-Xiao proved a formula about Lusztig's induction and restriction functors which can induce Green's formula for the path algebra of a quiver over a finite field via the trace map. In this paper, we generalize their formula to that for the mixed semisimple perverse sheaves for a quiver with an automorphism. By applying the trace map, we obtain Green's formula for any finite-dimensional hereditary algebra over a finite field.

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• Structure coefficients for quantum groups

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