Semi-skyline augmented fillings and non-symmetric Cauchy kernels for stair-type shapes
Autor(a) principal: | |
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Data de Publicação: | 2013 |
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/10316/44041 |
Resumo: | Using an analogue of the Robinson-Schensted-Knuth (RSK) algorithm for semi-skyline augmented fillings, due to Sarah Mason, we exhibit expansions of non-symmetric Cauchy kernels ∏(i,j)∈η(1−x_i y_j)−1, where the product is over all cell-coordinates (i,j) of the stair-type partition shape η, consisting of the cells in a NW-SE diagonal of a rectangle diagram and below it, containing the biggest stair shape. In the spirit of the classical Cauchy kernel expansion for rectangle shapes, this RSK variation provides an interpretation of the kernel for stair-type shapes as a family of pairs of semi-skyline augmented fillings whose key tableaux, determined by their shapes, lead to expansions as a sum of products of two families of key polynomials, the basis of Demazure characters of type A, and the Demazure atoms. A previous expansion of the Cauchy kernel in type A, for the stair shape was given by Alain Lascoux, based on the structure of double crystal graphs, and by Amy M. Fu and Alain Lascoux, relying on Demazure operators, which was also used to recover expansions for Ferrers shapes. |
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7160 |
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Semi-skyline augmented fillings and non-symmetric Cauchy kernels for stair-type shapesUsing an analogue of the Robinson-Schensted-Knuth (RSK) algorithm for semi-skyline augmented fillings, due to Sarah Mason, we exhibit expansions of non-symmetric Cauchy kernels ∏(i,j)∈η(1−x_i y_j)−1, where the product is over all cell-coordinates (i,j) of the stair-type partition shape η, consisting of the cells in a NW-SE diagonal of a rectangle diagram and below it, containing the biggest stair shape. In the spirit of the classical Cauchy kernel expansion for rectangle shapes, this RSK variation provides an interpretation of the kernel for stair-type shapes as a family of pairs of semi-skyline augmented fillings whose key tableaux, determined by their shapes, lead to expansions as a sum of products of two families of key polynomials, the basis of Demazure characters of type A, and the Demazure atoms. A previous expansion of the Cauchy kernel in type A, for the stair shape was given by Alain Lascoux, based on the structure of double crystal graphs, and by Amy M. Fu and Alain Lascoux, relying on Demazure operators, which was also used to recover expansions for Ferrers shapes.Discrete Mathematics & Theoretical Computer Science2013info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://hdl.handle.net/10316/44041http://hdl.handle.net/10316/44041enghttps://hal.inria.fr/hal-01229700/Azenhas, OlgaEmami, Araminfo: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:RCAAP2020-05-25T11:22:47Zoai:estudogeral.uc.pt:10316/44041Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T20:53:31.271708Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse |
dc.title.none.fl_str_mv |
Semi-skyline augmented fillings and non-symmetric Cauchy kernels for stair-type shapes |
title |
Semi-skyline augmented fillings and non-symmetric Cauchy kernels for stair-type shapes |
spellingShingle |
Semi-skyline augmented fillings and non-symmetric Cauchy kernels for stair-type shapes Azenhas, Olga |
title_short |
Semi-skyline augmented fillings and non-symmetric Cauchy kernels for stair-type shapes |
title_full |
Semi-skyline augmented fillings and non-symmetric Cauchy kernels for stair-type shapes |
title_fullStr |
Semi-skyline augmented fillings and non-symmetric Cauchy kernels for stair-type shapes |
title_full_unstemmed |
Semi-skyline augmented fillings and non-symmetric Cauchy kernels for stair-type shapes |
title_sort |
Semi-skyline augmented fillings and non-symmetric Cauchy kernels for stair-type shapes |
author |
Azenhas, Olga |
author_facet |
Azenhas, Olga Emami, Aram |
author_role |
author |
author2 |
Emami, Aram |
author2_role |
author |
dc.contributor.author.fl_str_mv |
Azenhas, Olga Emami, Aram |
description |
Using an analogue of the Robinson-Schensted-Knuth (RSK) algorithm for semi-skyline augmented fillings, due to Sarah Mason, we exhibit expansions of non-symmetric Cauchy kernels ∏(i,j)∈η(1−x_i y_j)−1, where the product is over all cell-coordinates (i,j) of the stair-type partition shape η, consisting of the cells in a NW-SE diagonal of a rectangle diagram and below it, containing the biggest stair shape. In the spirit of the classical Cauchy kernel expansion for rectangle shapes, this RSK variation provides an interpretation of the kernel for stair-type shapes as a family of pairs of semi-skyline augmented fillings whose key tableaux, determined by their shapes, lead to expansions as a sum of products of two families of key polynomials, the basis of Demazure characters of type A, and the Demazure atoms. A previous expansion of the Cauchy kernel in type A, for the stair shape was given by Alain Lascoux, based on the structure of double crystal graphs, and by Amy M. Fu and Alain Lascoux, relying on Demazure operators, which was also used to recover expansions for Ferrers shapes. |
publishDate |
2013 |
dc.date.none.fl_str_mv |
2013 |
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/10316/44041 http://hdl.handle.net/10316/44041 |
url |
http://hdl.handle.net/10316/44041 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
https://hal.inria.fr/hal-01229700/ |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.publisher.none.fl_str_mv |
Discrete Mathematics & Theoretical Computer Science |
publisher.none.fl_str_mv |
Discrete Mathematics & Theoretical Computer Science |
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) |
repository.name.fl_str_mv |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
repository.mail.fl_str_mv |
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1799133821647454208 |