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- Publisher Website: 10.1016/j.aim.2015.07.002
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Article: Green polynomials of Weyl groups, elliptic pairings, and the extended Dirac index
Title | Green polynomials of Weyl groups, elliptic pairings, and the extended Dirac index |
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Authors | |
Keywords | Dirac index Elliptic pairings Springer representations Weyl groups |
Issue Date | 2015 |
Citation | Advances in Mathematics, 2015, v. 283, p. 1-50 How to Cite? |
Abstract | In this paper, we give a uniform construction of irreducible genuine characters of the Pin cover W~ of a Weyl group W, and put them into the context of theory of Springer representations. In the process, we provide a direct connection between Springer theory, via Green polynomials, the irreducible representations of W~, and an extended Dirac operator for graded Hecke algebras. We also introduce a q-elliptic pairing for W with respect to the reflection representation V. These constructions are of independent interest. The q-elliptic pairing is a generalization of the elliptic pairing of W introduced by Reeder, and it is also related to S. Kato's notion of (graded) Kostka systems for the semidirect product AW=C[W]⋊S(V). |
Persistent Identifier | http://hdl.handle.net/10722/329367 |
ISSN | 2023 Impact Factor: 1.5 2023 SCImago Journal Rankings: 2.022 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Ciubotaru, Dan | - |
dc.contributor.author | He, Xuhua | - |
dc.date.accessioned | 2023-08-09T03:32:17Z | - |
dc.date.available | 2023-08-09T03:32:17Z | - |
dc.date.issued | 2015 | - |
dc.identifier.citation | Advances in Mathematics, 2015, v. 283, p. 1-50 | - |
dc.identifier.issn | 0001-8708 | - |
dc.identifier.uri | http://hdl.handle.net/10722/329367 | - |
dc.description.abstract | In this paper, we give a uniform construction of irreducible genuine characters of the Pin cover W~ of a Weyl group W, and put them into the context of theory of Springer representations. In the process, we provide a direct connection between Springer theory, via Green polynomials, the irreducible representations of W~, and an extended Dirac operator for graded Hecke algebras. We also introduce a q-elliptic pairing for W with respect to the reflection representation V. These constructions are of independent interest. The q-elliptic pairing is a generalization of the elliptic pairing of W introduced by Reeder, and it is also related to S. Kato's notion of (graded) Kostka systems for the semidirect product AW=C[W]⋊S(V). | - |
dc.language | eng | - |
dc.relation.ispartof | Advances in Mathematics | - |
dc.subject | Dirac index | - |
dc.subject | Elliptic pairings | - |
dc.subject | Springer representations | - |
dc.subject | Weyl groups | - |
dc.title | Green polynomials of Weyl groups, elliptic pairings, and the extended Dirac index | - |
dc.type | Article | - |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.1016/j.aim.2015.07.002 | - |
dc.identifier.scopus | eid_2-s2.0-84937846780 | - |
dc.identifier.volume | 283 | - |
dc.identifier.spage | 1 | - |
dc.identifier.epage | 50 | - |
dc.identifier.eissn | 1090-2082 | - |
dc.identifier.isi | WOS:000361016700001 | - |