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Factorization of the canonical bases for higher-level Fock spaces

  • Susumu Ariki (a1), Nicolas Jacon (a2) and Cédric Lecouvey (a3)

Abstract

The level l Fock space admits canonical bases and . They correspond to and -module structures. We establish that the transition matrices relating these two bases are unitriangular with coefficients in ℕ[v]. Restriction to the highest-weight modules generated by the empty l-partition then gives a natural quantization of a theorem by Geck and Rouquier on the factorization of decomposition matrices which are associated to Ariki–Koike algebras.

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Factorization of the canonical bases for higher-level Fock spaces

  • Susumu Ariki (a1), Nicolas Jacon (a2) and Cédric Lecouvey (a3)

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