Hodge-deligne polynomials of character varieties of free abelian groups
Autor(a) principal: | |
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Data de Publicação: | 2021 |
Outros Autores: | |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10400.21/13443 |
Resumo: | Let F be a finite group and X be a complex quasi-projective F-variety. For r is an element of N, we consider the mixed Hodge-Deligne polynomials of quotients X-r/F, where F acts diagonally, and compute them for certain classes of varieties X with simple mixed Hodge structures (MHSs). A particularly interesting case is when X is the maximal torus of an affine reductive group G, and F is its Weyl group. As an application, we obtain explicit formulas for the Hodge-Deligne and E-polynomials of (the distinguished component of) G-character varieties of free abelian groups. In the cases G = GL(n, C) and SL(n, C), we get even more concrete expressions for these polynomials, using the combinatorics of partitions. |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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Hodge-deligne polynomials of character varieties of free abelian groupsFree abelian groupCharacter varietyMixed Hodge structuresHodge-Deligne polynomialsEquivariant E-polynomialsFinite quotientsLet F be a finite group and X be a complex quasi-projective F-variety. For r is an element of N, we consider the mixed Hodge-Deligne polynomials of quotients X-r/F, where F acts diagonally, and compute them for certain classes of varieties X with simple mixed Hodge structures (MHSs). A particularly interesting case is when X is the maximal torus of an affine reductive group G, and F is its Weyl group. As an application, we obtain explicit formulas for the Hodge-Deligne and E-polynomials of (the distinguished component of) G-character varieties of free abelian groups. In the cases G = GL(n, C) and SL(n, C), we get even more concrete expressions for these polynomials, using the combinatorics of partitions.DE GRUYTER POLANDRCIPLFlorentinoSilva, Jaime2021-06-14T15:25:42Z2021-05-212021-05-21T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.21/13443engFLORENTINO, Carlos; SILVA, Jaime – Hodge-deligne polynomials of character varieties of free abelian groups. Open Mathematics. ISSN 2391-5455. Vol. 19, N.º 1 (2021), pp. 338-362.2391-545510.1515/math-2021-0038info:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-08-03T10:08:09ZPortal AgregadorONG |
dc.title.none.fl_str_mv |
Hodge-deligne polynomials of character varieties of free abelian groups |
title |
Hodge-deligne polynomials of character varieties of free abelian groups |
spellingShingle |
Hodge-deligne polynomials of character varieties of free abelian groups Florentino Free abelian group Character variety Mixed Hodge structures Hodge-Deligne polynomials Equivariant E-polynomials Finite quotients |
title_short |
Hodge-deligne polynomials of character varieties of free abelian groups |
title_full |
Hodge-deligne polynomials of character varieties of free abelian groups |
title_fullStr |
Hodge-deligne polynomials of character varieties of free abelian groups |
title_full_unstemmed |
Hodge-deligne polynomials of character varieties of free abelian groups |
title_sort |
Hodge-deligne polynomials of character varieties of free abelian groups |
author |
Florentino |
author_facet |
Florentino Silva, Jaime |
author_role |
author |
author2 |
Silva, Jaime |
author2_role |
author |
dc.contributor.none.fl_str_mv |
RCIPL |
dc.contributor.author.fl_str_mv |
Florentino Silva, Jaime |
dc.subject.por.fl_str_mv |
Free abelian group Character variety Mixed Hodge structures Hodge-Deligne polynomials Equivariant E-polynomials Finite quotients |
topic |
Free abelian group Character variety Mixed Hodge structures Hodge-Deligne polynomials Equivariant E-polynomials Finite quotients |
description |
Let F be a finite group and X be a complex quasi-projective F-variety. For r is an element of N, we consider the mixed Hodge-Deligne polynomials of quotients X-r/F, where F acts diagonally, and compute them for certain classes of varieties X with simple mixed Hodge structures (MHSs). A particularly interesting case is when X is the maximal torus of an affine reductive group G, and F is its Weyl group. As an application, we obtain explicit formulas for the Hodge-Deligne and E-polynomials of (the distinguished component of) G-character varieties of free abelian groups. In the cases G = GL(n, C) and SL(n, C), we get even more concrete expressions for these polynomials, using the combinatorics of partitions. |
publishDate |
2021 |
dc.date.none.fl_str_mv |
2021-06-14T15:25:42Z 2021-05-21 2021-05-21T00:00:00Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/10400.21/13443 |
url |
http://hdl.handle.net/10400.21/13443 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
FLORENTINO, Carlos; SILVA, Jaime – Hodge-deligne polynomials of character varieties of free abelian groups. Open Mathematics. ISSN 2391-5455. Vol. 19, N.º 1 (2021), pp. 338-362. 2391-5455 10.1515/math-2021-0038 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
DE GRUYTER POLAND |
publisher.none.fl_str_mv |
DE GRUYTER POLAND |
dc.source.none.fl_str_mv |
reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação instacron:RCAAP |
instname_str |
Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
instacron_str |
RCAAP |
institution |
RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
collection |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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repository.mail.fl_str_mv |
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1777304543791415296 |