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<p>In Fang et al.&#xa0;(J. Algebra <b>618</b>, 67–95 <CitationRef CitationID="CR8">2023</CitationRef>), 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.</p>

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The Parity of Lusztig’s Restriction Functor and Green’s Formula for a Quiver with Automorphism

  • 期刊论文

  • 发表日期：

    2025年3月4日

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  • Jiepeng Fang,
  • Yixin Lan,
  • Yumeng Wu

摘要

In Fang et al. (J. Algebra 618, 67–95 2023), 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.