Cherednik algebra for the normalizer

Henry Fallet

doi:10.5802/crmath.281

Théorie des représentations

Cherednik algebra for the normalizer

Henry Fallet ¹

¹ 33 Rue St Leu, 80000 Amiens, LAMFA, UMR 7352 CNRS-UPJV, France

Comptes Rendus. Mathématique, Volume 360 (2022), pp. 47-52.

Résumé

Ginzburg, Guay, Opdam and Rouquier established an equivalence of categories between a quotient category of the category $𝒪$ for the rational Cherednik algebra and the category of finite dimension modules of the Hecke algebra of a complex reflection group $W$ . We announce a generalization of this result to the extension of the Hecke algebra associated to the normalizer of a reflection subgroup.

Reçu le : 2021-04-29
Révisé le : 2021-07-06
Accepté le : 2021-10-09
Publié le : 2022-01-26

DOI : 10.5802/crmath.281

Classification : 20C08

Affiliations des auteurs :

Henry Fallet ¹

¹ 33 Rue St Leu, 80000 Amiens, LAMFA, UMR 7352 CNRS-UPJV, France

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     author = {Henry Fallet},
     title = {Cherednik algebra for the normalizer},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {47--52},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {360},
     year = {2022},
     doi = {10.5802/crmath.281},
     language = {en},
}

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Henry Fallet. Cherednik algebra for the normalizer. Comptes Rendus. Mathématique, Volume 360 (2022), pp. 47-52. doi : 10.5802/crmath.281. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.281/

Bibliographie
Cité par

[1] Gwyn Bellamy; Ulrich Thiel Highest weight theory for finite-dimensional graded algebras with triangular decomposition, Adv. Math., Volume 330 (2018), pp. 361-419 | DOI | MR | Zbl

[2] Cédric Bonnafé; Raphaël Rouquier Cherednik algebras and Calogero-Moser cells (2017) (https://arxiv.org/abs/1708.09764)

[3] Michel Broué; Gunter Malle; Raphaël Rouquier Complex reflection groups, braid groups, Hecke algebras, J. Reine Angew. Math., Volume 1998 (1998) no. 500, pp. 127-190 | MR | Zbl

[4] Rob C. Cannings; Martin P. Holland Differential operators on varieties with a quotient subvariety, J. Algebra, Volume 170 (1994) no. 3, pp. 735-753 | DOI | MR | Zbl

[5] Pavel Etingof Proof of the Broué–Malle–Rouquier conjecture in characteristic zero (after I. Losev and I. Marin-G. Pfeiffer), Arnold Math. J., Volume 3 (2017) no. 3, pp. 445-449 | DOI | Zbl

[6] Pavel Etingof; Victor Ginzburg Symplectic reflection algebras, Calogero-Moser space, and deformed Harish-Chandra homomorphism, Invent. Math., Volume 147 (2002) no. 2, pp. 243-348 | DOI | MR | Zbl

[7] Henry Fallet Opérateurs de Dunkl–Opdam, Catégorie $𝒪$ , Algèbres de Cherednik (PhD thesis in preparation at Université Picardie Jule-Verne)

[8] Victor Ginzburg Lectures on D-modules (1998) (Online lecture notes, available at Sabin Cautis’ webpage http://www. math. columbia. edu/~ scautis/dmodules/dmodules/ginzburg.pdf, with collaboration of Baranovsky, V. and Evens S)

[9] Victor Ginzburg; Nicolas Guay; Eric Opdam; Raphaël Rouquier On the category $𝒪$ for rational Cherednik algebras, Invent. Math., Volume 154 (2003) no. 3, pp. 617-651 | DOI | MR | Zbl

[10] Thomas Gobet; Anthony Henderson; Ivan Marin Braid groups of normalizers of reflection subgroups (2020) (https://arxiv.org/abs/2002.05468, to appear in Ann. Inst. Fourier)

[11] Thomas Gobet; Ivan Marin Hecke algebras of normalizers of parabolic subgroups (2020) (https://arxiv.org/abs/2006.09028)

[12] Claude Godbillon Eléments de topologie algébrique, Editions Hermann, 1971

[13] Randall R. Holmes; Daniel K. Nakano Brauer-type reciprocity for a class of graded associative algebras, J. Algebra, Volume 144 (1991) no. 1, pp. 117-126 | DOI | MR | Zbl

[14] Ivan Marin Artin groups and Yokonuma–Hecke algebras, Int. Math. Res. Not., Volume 2018 (2018) no. 13, pp. 4022-4062 | MR | Zbl

[15] Joseph J. Rotman An introduction to homological algebra, Springer, 2008

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