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Parabolic degeneration of rational Cherednik algebras

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Abstract

We introduce parabolic degenerations of rational Cherednik algebras of complex reflection groups, and use them to give necessary conditions for finite-dimensionality of an irreducible lowest weight module for the rational Cherednik algebra of a complex reflection group, and for the existence of a non-zero map between two standard modules. The latter condition reproduces and enhances, in the case of the symmetric group, the combinatorics of cores and dominance order, and in general shows that the c-ordering on category \(\mathcal {O}_c\) may be replaced by a much coarser ordering. The former gives a new proof of the classification of finite dimensional irreducible modules for the Cherednik algebra of the symmetric group.

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Authors and Affiliations

  1. Instituto de Matemática y Física, Universidad de Talca, Talca, Chile

    Stephen Griffeth & Armin Gusenbauer

  2. Institut de Mathématiques de Jussieu - Paris Rive Gauche (IMJ-PRG), CNRS UMR 6139, Université de Caen Basse-Normandie, 14032, Caen, France

    Daniel Juteau

  3. Dipartimento di Matematica, Università di Roma Tor Vergata, Rome, Italy

    Martina Lanini

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  1. Stephen Griffeth
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  2. Armin Gusenbauer
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Correspondence to Stephen Griffeth.

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Griffeth, S., Gusenbauer, A., Juteau, D. et al. Parabolic degeneration of rational Cherednik algebras. Sel. Math. New Ser. 23, 2705–2754 (2017). https://doi.org/10.1007/s00029-017-0337-3

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