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DC Field | Value | Language |
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dc.contributor.author | Polishchuk, Alexander | - |
dc.contributor.author | VAN DEN BERGH, Michel | - |
dc.date.accessioned | 2019-09-13T08:40:51Z | - |
dc.date.available | 2019-09-13T08:40:51Z | - |
dc.date.issued | 2019 | - |
dc.identifier.citation | JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, 21(9), p. 2653-2749 | - |
dc.identifier.issn | 1435-9855 | - |
dc.identifier.uri | http://hdl.handle.net/1942/29173 | - |
dc.description.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. | - |
dc.description.sponsorship | The first author is supported in part by the NSF grant DMS-1400390 and by the Russian Academic Excellence Project '5-100'. The second author is a senior researcher at the FWO and was supported by the FWO grant 1503512N. | - |
dc.language.iso | en | - |
dc.publisher | EUROPEAN MATHEMATICAL SOC | - |
dc.rights | European Mathematical Society 2019 | - |
dc.subject.other | Derived category; semiorthogonal decomposition; equivariant sheaf; Springer correspondence; reflection group; Hochschild homology; equivariant cohomology | - |
dc.subject.other | Derived category; semiorthogonal decomposition; equivariant sheaf; Springer correspondence; reflection group; Hochschild homology; equivariant cohomology | - |
dc.title | Semiorthogonal decompositions of the categories of equivariant coherent sheaves for some reflection groups | - |
dc.type | Journal Contribution | - |
dc.identifier.epage | 2749 | - |
dc.identifier.issue | 9 | - |
dc.identifier.spage | 2653 | - |
dc.identifier.volume | 21 | - |
local.format.pages | 97 | - |
local.bibliographicCitation.jcat | A1 | - |
dc.description.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. | - |
local.publisher.place | ZURICH | - |
local.type.refereed | Refereed | - |
local.type.specified | Article | - |
dc.identifier.doi | 10.4171/JEMS/890 | - |
dc.identifier.isi | 000476473900002 | - |
item.contributor | Polishchuk, Alexander | - |
item.contributor | VAN DEN BERGH, Michel | - |
item.fullcitation | Polishchuk, Alexander & VAN DEN BERGH, Michel (2019) Semiorthogonal decompositions of the categories of equivariant coherent sheaves for some reflection groups. In: JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, 21(9), p. 2653-2749. | - |
item.accessRights | Open Access | - |
item.fulltext | With Fulltext | - |
item.validation | ecoom 2020 | - |
crisitem.journal.issn | 1435-9855 | - |
Appears in Collections: | Research publications |
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polishchuk2019.pdf Restricted Access | Published version | 572.47 kB | Adobe PDF | View/Open Request a copy |
polishchuk_vdb.pdf | Peer-reviewed author version | 891.78 kB | Adobe PDF | View/Open |
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