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Equivariant Tilting Modules, Pfaffian Varieties and Noncommutative Matrix Factorizations
Yuki Hirano Department of Mathematics, Kyoto University, Kitashirakawa-Oiwake-cho, Sakyo-ku, Kyoto, 606-8502, Japan
Abstract:
We show that equivariant tilting modules over equivariant algebras induce equivalences of derived factorization categories. As an application, we show that the derived category of a noncommutative resolution of a linear section of a Pfaffian variety is equivalent to the derived factorization category of a noncommutative gauged Landau–Ginzburg model $(\Lambda,\chi, w)^{\mathbb{G}_m}$, where $\Lambda$ is a noncommutative resolution of the quotient singularity $W/\operatorname{GSp}(Q)$ arising from a certain representation $W$ of the symplectic similitude group $\operatorname{GSp}(Q)$ of a symplectic vector space $Q$.
Keywords:
equivariant tilting module, Pfaffian variety, matrix factorization.
Received: September 29, 2020; in final form May 28, 2021; Published online June 2, 2021
Citation:
Yuki Hirano, “Equivariant Tilting Modules, Pfaffian Varieties and Noncommutative Matrix Factorizations”, SIGMA, 17 (2021), 055, 43 pp.
Linking options:
https://www.mathnet.ru/eng/sigma1738 https://www.mathnet.ru/eng/sigma/v17/p55
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Abstract page: | 56 | Full-text PDF : | 20 | References: | 13 |
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