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arXiv:2406.03238 [math.RT]AbstractReferencesReviewsResources

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

Jiepeng Fang, Yixin Lan, Yumeng Wu

Published 2024-06-05Version 1

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.

Categories: math.RT, math.QA, math.RA
Subjects: 16G20, 17B37
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