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Symmetry, Integrability and Geometry: Methods and Applications, 2021, Volume 17, 055, 43 pp.
DOI: https://doi.org/10.3842/SIGMA.2021.055
(Mi sigma1738)
 

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
References:
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.
Funding agency Grant number
Japan Society for the Promotion of Science 19K14502
The author is supported by JSPS KAKENHI 19K14502.
Received: September 29, 2020; in final form May 28, 2021; Published online June 2, 2021
Bibliographic databases:
Document Type: Article
MSC: 14F08, 18G80, 16E35
Language: English
Citation: Yuki Hirano, “Equivariant Tilting Modules, Pfaffian Varieties and Noncommutative Matrix Factorizations”, SIGMA, 17 (2021), 055, 43 pp.
Citation in format AMSBIB
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\by Yuki~Hirano
\paper Equivariant Tilting Modules, Pfaffian Varieties and Noncommutative Matrix Factorizations
\jour SIGMA
\yr 2021
\vol 17
\papernumber 055
\totalpages 43
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\crossref{https://doi.org/10.3842/SIGMA.2021.055}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85108581792}
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