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Title: | Semiorthogonal decompositions of the categories of equivariant coherent sheaves for some reflection groups | Authors: | Polishchuk, Alexander VAN DEN BERGH, Michel |
Issue Date: | 2019 | Publisher: | EUROPEAN MATHEMATICAL SOC | Source: | JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, 21(9), p. 2653-2749 | Abstract: | We consider the derived category D-G(b)(V) of coherent sheaves on a complex vector space V equivariant with respect to an action of a finite reflection group G. In some cases, including Weyl groups of type A, B, G(2), F-4, as well as the groups G(m, 1, n) = (mu(m))(n) (sic) S-n, we construct a semiorthogonal decomposition of this category, indexed by the conjugacy classes of G. The pieces of this decompositions are equivalent to the derived categories of coherent sheaves on the quotient-spaces V-g/C(g), where C(g) is the centralizer subgroup of g is an element of G. In the case of the Weyl groups the construction uses some key results about the Springer correspondence, due to Lusztig, along with some formality statement generalizing a result of Deligne [23]. We also construct global analogs of some of these semiorthogonal decompositions involving derived categories of equivariant coherent sheaves on C-n, where C is a smooth curve. | Notes: | [Polishchuk, Alexander] Univ Oregon, Dept Math, Eugene, OR 97403 USA. [Polishchuk, Alexander] Natl Res Univ, Higher Sch Econ, Moscow, Russia. [Van den Bergh, Michel] Univ Hasselt, Dept WNI, Univ Campus, B-3590 Diepenbeek, Belgium. | Keywords: | Derived category; semiorthogonal decomposition; equivariant sheaf; Springer correspondence; reflection group; Hochschild homology; equivariant cohomology;Derived category; semiorthogonal decomposition; equivariant sheaf; Springer correspondence; reflection group; Hochschild homology; equivariant cohomology | Document URI: | http://hdl.handle.net/1942/29173 | ISSN: | 1435-9855 | DOI: | 10.4171/JEMS/890 | ISI #: | 000476473900002 | Rights: | European Mathematical Society 2019 | Category: | A1 | Type: | Journal Contribution | Validations: | ecoom 2020 |
Appears in Collections: | Research publications |
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