Relevant bibliographies by topics / Alvis-Curtis duality

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  1. Journal articles
  2. Dissertations / Theses

Academic literature on the topic 'Alvis-Curtis duality'

Author: Grafiati
Published: 14 December 2024

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Journal articles on the topic "Alvis-Curtis duality"

1

Dong, Junbin. "Alvis–Curtis duality for representations of reductive groups with Frobenius maps." Forum Mathematicum 32, no. 5 (September 1, 2020): 1289–96. http://dx.doi.org/10.1515/forum-2020-0053.

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AbstractWe generalize the Alvis–Curtis duality to the abstract representations of reductive groups with Frobenius maps. Similar to the case of representations of finite reductive groups, we show that the Alvis–Curtis duality of infinite type, which we define in this paper, also interchanges the irreducible representations in the principal representation category.
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2

ACKERMANN, BERND, and SIBYLLE SCHROLL. "On decomposition numbers and Alvis–Curtis duality." Mathematical Proceedings of the Cambridge Philosophical Society 143, no. 3 (November 2007): 509–20. http://dx.doi.org/10.1017/s0305004107000667.

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AbstractWe show that for general linear groups GLn(q) as well as for q-Schur algebras the knowledge of the modular Alvis–Curtis duality over fields of characteristic ℓ, ℓ ∤ q, is equivalent to the knowledge of the decomposition numbers.
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3

Cabanes, Marc. "On Okuyama’s Theorems about Alvis-Curtis Duality." Nagoya Mathematical Journal 195 (2009): 1–19. http://dx.doi.org/10.1017/s0027763000009673.

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AbstractWe report on theorems by T. Okuyama about complexes generalizing the Coxeter complex and the action of parabolic subgroups on them, both for finite BN-pairs and finite dimensional Hecke algebras. Several simplifications, using mainly the surjections of [CaRi], allow a more compact treatment than the one in [O].
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4

Schroll, Sibylle. "ALVIS–CURTIS DUALITY ON LOWERCASE q-SCHUR AND HECKE ALGEBRAS." Quarterly Journal of Mathematics 58, no. 2 (October 19, 2006): 255–63. http://dx.doi.org/10.1093/qmath/hal022.

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5

LINCKELMANN, MARKUS, and SIBYLLE SCHROLL. "ON THE COXETER COMPLEX AND ALVIS–CURTIS DUALITY FOR PRINCIPAL ℓ-BLOCKS OF GLn(q)." Journal of Algebra and Its Applications 04, no. 03 (June 2005): 225–29. http://dx.doi.org/10.1142/s0219498805001198.

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M. Cabanes and J. Rickard showed in [3] that the Alvis–Curtis character duality of a finite group of Lie type is induced in non defining characteristic ℓ by a derived equivalence given by tensoring with a bounded complex X, and they further conjecture that this derived equivalence should actually be a homotopy equivalence. Following a suggestion of R. Kessar, we show here for the special case of principal blocks of general linear groups with abelian Sylow-ℓ-subgroups that this is true, by an explicit verification relating the complex X to the Coxeter complex of the corresponding Weyl group.
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6

Schroll, S., and K. M. Tan. "Weight 2 Blocks of General Linear Groups and Modular Alvis-Curtis Duality." International Mathematics Research Notices, July 8, 2010. http://dx.doi.org/10.1093/imrn/rnm130.

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7

Dudas, Olivier, and Nicolas Jacon. "Alvis-Curtis Duality for Finite General Linear Groups and a Generalized Mullineux Involution." Symmetry, Integrability and Geometry: Methods and Applications, January 30, 2018. http://dx.doi.org/10.3842/sigma.2018.007.

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Dissertations / Theses on the topic "Alvis-Curtis duality"

1

Qin, Chuan. "Involution pour les représentations des algèbres de Hecke." Electronic Thesis or Diss., Sorbonne université, 2024. http://www.theses.fr/2024SORUS291.

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Dans cette thèse, nous présentons deux généralisations de la dualité d'Alvis-Curtis au cas des algèbres de Hecke : une version relative pour les algèbres de Hecke finies, basée sur le travail de Howlett-Lehrer, et une version à paramètres inégaux pour les algèbres de Hecke affines, basée sur le travail de S.-I. Kato (qui, sous certaines hypothèses, correspond à la dualité d'Aubert-Zelevinsky pour les représentations irréductibles lisses complexes de groupes p-adiques). Nous démontrons ensuite leur compatibilité avec la dualité d'Aubert-Zelevinsky lorsqu'elles sont restreintes à certains blocs de Bernstein. Enfin, motivés par le travail récent d'Aubert-Xu, nous fournissons des exemples de calculs du foncteur de dualité pour les séries principales du groupe exceptionnel G2
In this thesis, we give two generalizations of the Alvis-Curtis duality for Hecke algebras: a relative version for finite Hecke algebras, based on Howlett-Lehrer's work, and an unequal parameter version for affine Hecke algebras, based on S-I. Kato's work (which under certain assumptions, corresponds to the Aubert-Zelevinsky duality for complex smooth irreducible representations of p-adic groups). Then, we prove their compatibility with the Aubert-Zelevinsky duality when restricted to some Bernstein blocks. Finally, motivated by the recent work of Aubert-Xu, we provide examples of calculations of the duality functor for the principal series of the exceptional group G2
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