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Article: P-alcoves, parabolic subalgebras and cocenters of affine Hecke algebras
Title | P-alcoves, parabolic subalgebras and cocenters of affine Hecke algebras |
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Authors | |
Keywords | Affine Hecke algebras Cocenters Parabolic subalgebras |
Issue Date | 2015 |
Citation | Selecta Mathematica, New Series, 2015, v. 21, n. 3, p. 995-1019 How to Cite? |
Abstract | The cocenter of an affine Hecke algebra plays an important role in the study of representations of the affine Hecke algebra and the geometry of affine Deligne–Lusztig varieties (see for example, He and Nie in Compos Math 150(11):1903–1927, 2014; He in Ann Math 179:367–404, 2014; Ciubotaru and He in Cocenter and representations of affine Hecke algebras, 2014). In this paper, we give a Bernstein–Lusztig type presentation of the cocenter. We also obtain a comparison theorem between the class polynomials of the affine Hecke algebra and those of its parabolic subalgebras, which is an algebraic analog of the Hodge–Newton decomposition theorem for affine Deligne–Lusztig varieties. As a consequence, we present a new proof of the emptiness pattern of affine Deligne–Lusztig varieties (Görtz et al. in Compos Math 146(5):1339–1382, 2010; Görtz et al. in Ann Sci Ècole Norm Sup, 2012). |
Persistent Identifier | http://hdl.handle.net/10722/329366 |
ISSN | 2023 Impact Factor: 1.2 2023 SCImago Journal Rankings: 1.715 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | He, Xuhua | - |
dc.contributor.author | Nie, Sian | - |
dc.date.accessioned | 2023-08-09T03:32:16Z | - |
dc.date.available | 2023-08-09T03:32:16Z | - |
dc.date.issued | 2015 | - |
dc.identifier.citation | Selecta Mathematica, New Series, 2015, v. 21, n. 3, p. 995-1019 | - |
dc.identifier.issn | 1022-1824 | - |
dc.identifier.uri | http://hdl.handle.net/10722/329366 | - |
dc.description.abstract | The cocenter of an affine Hecke algebra plays an important role in the study of representations of the affine Hecke algebra and the geometry of affine Deligne–Lusztig varieties (see for example, He and Nie in Compos Math 150(11):1903–1927, 2014; He in Ann Math 179:367–404, 2014; Ciubotaru and He in Cocenter and representations of affine Hecke algebras, 2014). In this paper, we give a Bernstein–Lusztig type presentation of the cocenter. We also obtain a comparison theorem between the class polynomials of the affine Hecke algebra and those of its parabolic subalgebras, which is an algebraic analog of the Hodge–Newton decomposition theorem for affine Deligne–Lusztig varieties. As a consequence, we present a new proof of the emptiness pattern of affine Deligne–Lusztig varieties (Görtz et al. in Compos Math 146(5):1339–1382, 2010; Görtz et al. in Ann Sci Ècole Norm Sup, 2012). | - |
dc.language | eng | - |
dc.relation.ispartof | Selecta Mathematica, New Series | - |
dc.subject | Affine Hecke algebras | - |
dc.subject | Cocenters | - |
dc.subject | Parabolic subalgebras | - |
dc.title | P-alcoves, parabolic subalgebras and cocenters of affine Hecke algebras | - |
dc.type | Article | - |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.1007/s00029-014-0170-x | - |
dc.identifier.scopus | eid_2-s2.0-84937250701 | - |
dc.identifier.volume | 21 | - |
dc.identifier.issue | 3 | - |
dc.identifier.spage | 995 | - |
dc.identifier.epage | 1019 | - |
dc.identifier.eissn | 1420-9020 | - |
dc.identifier.isi | WOS:000357494400006 | - |