Enumerating projective reflection groups
International audience Projective reflection groups have been recently defined by the second author. They include a special class of groups denoted G(r,p,s,n) which contains all classical Weyl groups and more generally all the complex reflection groups of type G(r,p,n). In this paper we define some...
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ftunivstetienne:oai:HAL:hal-01215079v1 2024-09-15T18:14:15+00:00 Enumerating projective reflection groups Biagioli, Riccardo Caselli, Fabrizio Institut Camille Jordan (ICJ) École Centrale de Lyon (ECL) Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL) Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon) Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet - Saint-Étienne (UJM)-Centre National de la Recherche Scientifique (CNRS) Dipartimento di Matematica Bologna Alma Mater Studiorum Università di Bologna = University of Bologna (UNIBO) Bousquet-Mélou Mireille and Wachs Michelle and Hultman Axel Reykjavik, Iceland 2011 https://inria.hal.science/hal-01215079 https://inria.hal.science/hal-01215079/document https://inria.hal.science/hal-01215079/file/dmAO0114.pdf https://doi.org/10.46298/dmtcs.2898 en eng HAL CCSD Discrete Mathematics and Theoretical Computer Science DMTCS info:eu-repo/semantics/altIdentifier/doi/10.46298/dmtcs.2898 hal-01215079 https://inria.hal.science/hal-01215079 https://inria.hal.science/hal-01215079/document https://inria.hal.science/hal-01215079/file/dmAO0114.pdf doi:10.46298/dmtcs.2898 info:eu-repo/semantics/OpenAccess ISSN: 1462-7264 EISSN: 1365-8050 Discrete Mathematics and Theoretical Computer Science Discrete Mathematics and Theoretical Computer Science (DMTCS) 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011) https://inria.hal.science/hal-01215079 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011), 2011, Reykjavik, Iceland. pp.147-158, ⟨10.46298/dmtcs.2898⟩ reflection groups characters permutation statistics generating functions [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO] [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM] info:eu-repo/semantics/conferenceObject Conference papers 2011 ftunivstetienne https://doi.org/10.46298/dmtcs.2898 2024-07-09T00:05:39Z International audience Projective reflection groups have been recently defined by the second author. They include a special class of groups denoted G(r,p,s,n) which contains all classical Weyl groups and more generally all the complex reflection groups of type G(r,p,n). In this paper we define some statistics analogous to descent number and major index over the projective reflection groups G(r,p,s,n), and we compute several generating functions concerning these parameters. Some aspects of the representation theory of G(r,p,s,n), as distribution of one-dimensional characters and computation of Hilbert series of some invariant algebras, are also treated. Les groupes de réflexions projectifs ont été récemment définis par le deuxième auteur. Ils comprennent une classe spéciale de groupes notée G(r,p,s,n), qui contient tous les groupes de Weyl classiques et plus généralement tous les groupes de réflexions complexes du type G(r,p,n). Dans ce papier on définit des statistiques analogues au nombre de descentes et à l'indice majeur pour les groupes G(r,p,s,n), et on calcule plusieurs fonctions génératrices. Certains aspects de la théorie des représentations de G(r,p,s,n), comme la distribution des caractères linéaires et le calcul de la série de Hilbert de quelques algèbres d'invariants, sont aussi abordés. Conference Object Iceland Université Jean Monnet – Saint-Etienne: HAL Discrete Mathematics & Theoretical Computer Science DMTCS Proceeding Proceedings |
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Université Jean Monnet – Saint-Etienne: HAL |
op_collection_id |
ftunivstetienne |
language |
English |
topic |
reflection groups characters permutation statistics generating functions [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO] [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM] |
spellingShingle |
reflection groups characters permutation statistics generating functions [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO] [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM] Biagioli, Riccardo Caselli, Fabrizio Enumerating projective reflection groups |
topic_facet |
reflection groups characters permutation statistics generating functions [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO] [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM] |
description |
International audience Projective reflection groups have been recently defined by the second author. They include a special class of groups denoted G(r,p,s,n) which contains all classical Weyl groups and more generally all the complex reflection groups of type G(r,p,n). In this paper we define some statistics analogous to descent number and major index over the projective reflection groups G(r,p,s,n), and we compute several generating functions concerning these parameters. Some aspects of the representation theory of G(r,p,s,n), as distribution of one-dimensional characters and computation of Hilbert series of some invariant algebras, are also treated. Les groupes de réflexions projectifs ont été récemment définis par le deuxième auteur. Ils comprennent une classe spéciale de groupes notée G(r,p,s,n), qui contient tous les groupes de Weyl classiques et plus généralement tous les groupes de réflexions complexes du type G(r,p,n). Dans ce papier on définit des statistiques analogues au nombre de descentes et à l'indice majeur pour les groupes G(r,p,s,n), et on calcule plusieurs fonctions génératrices. Certains aspects de la théorie des représentations de G(r,p,s,n), comme la distribution des caractères linéaires et le calcul de la série de Hilbert de quelques algèbres d'invariants, sont aussi abordés. |
author2 |
Institut Camille Jordan (ICJ) École Centrale de Lyon (ECL) Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL) Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon) Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet - Saint-Étienne (UJM)-Centre National de la Recherche Scientifique (CNRS) Dipartimento di Matematica Bologna Alma Mater Studiorum Università di Bologna = University of Bologna (UNIBO) Bousquet-Mélou Mireille and Wachs Michelle and Hultman Axel |
format |
Conference Object |
author |
Biagioli, Riccardo Caselli, Fabrizio |
author_facet |
Biagioli, Riccardo Caselli, Fabrizio |
author_sort |
Biagioli, Riccardo |
title |
Enumerating projective reflection groups |
title_short |
Enumerating projective reflection groups |
title_full |
Enumerating projective reflection groups |
title_fullStr |
Enumerating projective reflection groups |
title_full_unstemmed |
Enumerating projective reflection groups |
title_sort |
enumerating projective reflection groups |
publisher |
HAL CCSD |
publishDate |
2011 |
url |
https://inria.hal.science/hal-01215079 https://inria.hal.science/hal-01215079/document https://inria.hal.science/hal-01215079/file/dmAO0114.pdf https://doi.org/10.46298/dmtcs.2898 |
op_coverage |
Reykjavik, Iceland |
genre |
Iceland |
genre_facet |
Iceland |
op_source |
ISSN: 1462-7264 EISSN: 1365-8050 Discrete Mathematics and Theoretical Computer Science Discrete Mathematics and Theoretical Computer Science (DMTCS) 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011) https://inria.hal.science/hal-01215079 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011), 2011, Reykjavik, Iceland. pp.147-158, ⟨10.46298/dmtcs.2898⟩ |
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info:eu-repo/semantics/altIdentifier/doi/10.46298/dmtcs.2898 hal-01215079 https://inria.hal.science/hal-01215079 https://inria.hal.science/hal-01215079/document https://inria.hal.science/hal-01215079/file/dmAO0114.pdf doi:10.46298/dmtcs.2898 |
op_rights |
info:eu-repo/semantics/OpenAccess |
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https://doi.org/10.46298/dmtcs.2898 |
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Discrete Mathematics & Theoretical Computer Science |
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DMTCS Proceeding |
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