q-Schur algebras and complex reflection groups, I

By Raphaël Rouquier. 2005

217 citations recorded by the source corpus.

We show that the category O for a rational Cherednik algebra of type A is equivalent to modules over a q-Schur algebra (parameter not a half integer), providing thus character formulas for simple modules. We give some generalization to B_n(d). We prove an ``abstract'' translation principle. These results follow from the unicity of certain highest categories covering Hecke algebras. We also provide a semi-simplicity criterion for Hecke algebras of complex reflection groups.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/043c39c053645c1f4a3c2caac88b40fea7295721

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In Discrete Mathematics and Combinatorics

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Surveys in Combinatorics 2011: The cyclic sieving phenomenon: a survey (2010, background): “The primary ingredients of their construction are Rouquier’s formulation of shift functors for the rational Cherednik algebras of W [64], and Opdam’s analysis of permutations of the irreducible representations of W arising from the Knizhnik-Zamolodchikov connection [51].”
Khovanov homology is a skew Howe 2-representation of categorified quantum sl(m) (2012, methodology): “A key part of this structure is that F is a left and right adjoint for E and that the endomorphisms of E are acted upon by the so-called KLR algebras developed in papers by Chuang and Rouquier [21], Khovanov and Lauda [36; 38] and Rouquier [64].”
Catalan numbers for complex reflection groups (2009, methodology): “Our key tools are the equivalences of highest weight categories discovered by Rouquier in [13] and Opdam’s study of the monodromy of the Knizhnik-Zamalodchikov connection in [10].”