Schur–Weyl duality for higher levels

• Jonathan Brundan ^[1] ; Alexander Kleshchev ^[1]
  1. [1] Department of Mathematics, University of Oregon, USA
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 14, Nº. 1, 2008, págs. 1-57
• Idioma: inglés
• DOI: 10.1007/s00029-008-0059-7
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• Resumen

  • We extend Schur–Weyl duality to an arbitrary level l ≥ 1, level one recovering the classical duality between the symmetric and general linear groups. In general, the symmetric group is replaced by the degenerate cyclotomic Hecke algebra over C parametrized by a dominant weight of level l for the root system of type A∞. As an application, we prove that the degenerate analogue of the quasi-hereditary cover of the cyclotomic Hecke algebra constructed by Dipper, James and Mathas is Morita equivalent to certain blocks of parabolic category O for the general linear Lie algebra.