The parity of Lusztig's restriction functor and Green's formula for a quiver with automorphism
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| Format: | Preprint |
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2024
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| _version_ | 1866916275645579264 |
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| author | Fang, Jiepeng Lan, Yixin Wu, Yumeng |
| author_facet | Fang, Jiepeng Lan, Yixin Wu, Yumeng |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2406_03238 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The parity of Lusztig's restriction functor and Green's formula for a quiver with automorphism Fang, Jiepeng Lan, Yixin Wu, Yumeng Representation Theory Quantum Algebra Rings and Algebras 16G20, 17B37 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. |
| title | The parity of Lusztig's restriction functor and Green's formula for a quiver with automorphism |
| topic | Representation Theory Quantum Algebra Rings and Algebras 16G20, 17B37 |
| url | https://arxiv.org/abs/2406.03238 |