An algebraic approach to the KZ-functor for rational Cherednik algebras associated with cyclic groups

2016/02/25 by Sam Thelin, Thelin, Sam
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology #math.RT #msc:16G99

paper · pdf · doi:10.48550/arxiv.1602.08029

31 pages

arxiv created 2016/02/25 · arxiv updated 2016/02/26

Abstract

In the case of rational Cherednik algebras associated with cyclic groups, we give an alternative proof that the projective object P_KZ representing the KZ-functor is isomorphic to the Δ-module associated with the coinvariant algebra for a subset of parameter values from which all parameter values can be obtained by integral translations. We also specify the exact parameter values for which this isomorphism occurs. Furthermore, we determine the action of the cyclotomic Hecke algebra on P_KZ for these parameter values, thereby giving a complete algebraic description of the KZ-functor in this case.

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