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Semiorthogonal decompositions of the categories of equivariant coherent sheaves for some reflection groups

Journal Contribution - Journal Article

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.
Journal: JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY
ISSN: 1435-9855
Issue: 9
Volume: 21
Pages: 2653 - 2749
Publication year:2019
Keywords:Derived category, semiorthogonal decomposition, equivariant sheaf, Springer correspondence, reflection group, Hochschild homology, equivariant cohomology
BOF-keylabel:yes
IOF-keylabel:yes
BOF-publication weight:6
CSS-citation score:2
Authors:International
Authors from:Higher Education
Accessibility:Open