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Article: Minimal length elements of extended affine Weyl groups
Title | Minimal length elements of extended affine Weyl groups |
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Authors | |
Keywords | affine Hecke algebras affine Weyl groups minimal length elements |
Issue Date | 2014 |
Citation | Compositio Mathematica, 2014, v. 150, n. 11, p. 1903-1927 How to Cite? |
Abstract | Let W be an extended affine Weyl group. We prove that the minimal length elements wO of any conjugacy class O of W satisfy some nice properties, generalizing results of Geck and Pfeiffer [On the irreducible characters of Hecke algebras, Adv. Math. 102 (1993), 79-94] on finite Weyl groups. We also study a special class of conjugacy classes, the straight conjugacy classes. These conjugacy classes are in a natural bijection with the Frobenius-twisted conjugacy classes of some $p$-adic group and satisfy additional interesting properties. Furthermore, we discuss some applications to the affine Hecke algebra H. We prove that TwO, where O ranges over all the conjugacy classes of W, forms a basis of the cocenter H/[H,H]. We also introduce the class polynomials, which play a crucial role in the study of affine Deligne-Lusztig varieties He [Geometric and cohomological properties of affine Deligne-Lusztig varieties, Ann. of Math. (2) 179 (2014), 367-404]. |
Persistent Identifier | http://hdl.handle.net/10722/329341 |
ISSN | 2023 Impact Factor: 1.3 2023 SCImago Journal Rankings: 2.490 |
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 | 2023-08-09T03:32:06Z | - |
dc.date.available | 2023-08-09T03:32:06Z | - |
dc.date.issued | 2014 | - |
dc.identifier.citation | Compositio Mathematica, 2014, v. 150, n. 11, p. 1903-1927 | - |
dc.identifier.issn | 0010-437X | - |
dc.identifier.uri | http://hdl.handle.net/10722/329341 | - |
dc.description.abstract | Let W be an extended affine Weyl group. We prove that the minimal length elements wO of any conjugacy class O of W satisfy some nice properties, generalizing results of Geck and Pfeiffer [On the irreducible characters of Hecke algebras, Adv. Math. 102 (1993), 79-94] on finite Weyl groups. We also study a special class of conjugacy classes, the straight conjugacy classes. These conjugacy classes are in a natural bijection with the Frobenius-twisted conjugacy classes of some $p$-adic group and satisfy additional interesting properties. Furthermore, we discuss some applications to the affine Hecke algebra H. We prove that TwO, where O ranges over all the conjugacy classes of W, forms a basis of the cocenter H/[H,H]. We also introduce the class polynomials, which play a crucial role in the study of affine Deligne-Lusztig varieties He [Geometric and cohomological properties of affine Deligne-Lusztig varieties, Ann. of Math. (2) 179 (2014), 367-404]. | - |
dc.language | eng | - |
dc.relation.ispartof | Compositio Mathematica | - |
dc.subject | affine Hecke algebras | - |
dc.subject | affine Weyl groups | - |
dc.subject | minimal length elements | - |
dc.title | Minimal length elements of extended affine Weyl groups | - |
dc.type | Article | - |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.1112/S0010437X14007349 | - |
dc.identifier.scopus | eid_2-s2.0-84911485403 | - |
dc.identifier.volume | 150 | - |
dc.identifier.issue | 11 | - |
dc.identifier.spage | 1903 | - |
dc.identifier.epage | 1927 | - |
dc.identifier.isi | WOS:000345188400005 | - |