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arXiv · 2406.03238

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

Jiepeng Fang·Yixin Lan·Yumeng Wu
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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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Jiepeng Fang, Yixin Lan, Yumeng Wu. 2024-06-05. The parity of Lusztig's restriction functor and Green's formula for a quiver with automorphism. https://arxiv.org/abs/2406.03238

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