Algebra & Number Theory

Finite-dimensional quotients of Hecke algebras

Ivan Losev

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Abstract

Let W be a complex reflection group. We prove that there is a maximal finite-dimensional quotient of the Hecke algebra q(W) of W, and that the dimension of this quotient coincides with |W|. This is a weak version of a 1998 Broué–Malle–Rouquier conjecture. The proof is based on the categories O for rational Cherednik algebras.

Article information

Source
Algebra Number Theory, Volume 9, Number 2 (2015), 493-502.

Dates
Received: 13 August 2014
Accepted: 18 February 2015
First available in Project Euclid: 16 November 2017

Permanent link to this document
https://projecteuclid.org/euclid.ant/1510842289

Digital Object Identifier
doi:10.2140/ant.2015.9.493

Mathematical Reviews number (MathSciNet)
MR3320850

Zentralblatt MATH identifier
1323.20008

Subjects
Primary: 20C08: Hecke algebras and their representations
Secondary: 20F55: Reflection and Coxeter groups [See also 22E40, 51F15] 16G99: None of the above, but in this section

Keywords
Hecke algebras rational Cherednik algebras categories $\mathcal O$ KZ functor

Citation

Losev, Ivan. Finite-dimensional quotients of Hecke algebras. Algebra Number Theory 9 (2015), no. 2, 493--502. doi:10.2140/ant.2015.9.493. https://projecteuclid.org/euclid.ant/1510842289


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References

  • R. Bezrukavnikov and P. Etingof, “Parabolic induction and restriction functors for rational Cherednik algebras”, Selecta Math. $($N.S.$)$ 14:3-4 (2009), 397–425.
  • M. Broué, G. Malle, and R. Rouquier, “Complex reflection groups, braid groups, Hecke algebras”, J. Reine Angew. Math. 500 (1998), 127–190.
  • P. Etingof and V. Ginzburg, “Symplectic reflection algebras, Calogero–Moser space, and deformed Harish-Chandra homomorphism”, Invent. Math. 147:2 (2002), 243–348.
  • P. Etingof, E. Gorsky, and I. Losev, “Representations of rational Cherednik algebras with minimal support and torus knots”, preprint, 2013.
  • V. Ginzburg, N. Guay, E. Opdam, and R. Rouquier, “On the category $\mathscr O$ for rational Cherednik algebras”, Invent. Math. 154:3 (2003), 617–651.
  • I. Marin, “The freeness conjecture for Hecke algebras of complex reflection groups, and the case of the Hessian group $G\sb {26}$”, J. Pure Appl. Algebra 218:4 (2014), 704–720.
  • R. Rouquier, “$q$-Schur algebras and complex reflection groups”, Mosc. Math. J. 8:1 (2008), 119–158.
  • A. Grothendieck, Cohomologie locale des faisceaux cohérents et théorèmes de Lefschetz locaux et globaux (Séminaire de Géométrie Algébrique du Bois Marie 1962 $=$ SGA,2), Advanced Stud. in Pure Math. 2, North-Holland, Amsterdam, 1968.
  • G. C. Shephard and J. A. Todd, “Finite unitary reflection groups”, Canadian J. Math. 6 (1954), 274–304.
  • S. Wilcox, “Supports of representations of the rational Cherednik algebra of type A”, preprint, 2011.