Parabolic degeneration of rational Cherednik algebras

• Stephen Griffeth ^[1] ; Armin Gusenbauer ^[1] ; Daniel Juteau ^[2] ; Martina Lanini ^[3]
  1. [1] Universidad de Talca

     Universidad de Talca

     Provincia de Talca, Chile

     
  2. [2] Université de Caen Basse-Normandie
  3. [3] Università di Roma Tor Vergata

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• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 23, Nº. 4, 2017, págs. 2705-2754
• Idioma: inglés
• DOI: 10.1007/s00029-017-0337-3
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• Resumen

  • We introduce parabolic degenerations of rational Cherednik algebras of complex reflection groups, and use them to give necessary conditions for finitedimensionality 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 Oc 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.