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Factorization of the canonical bases for higher-level Fock spaces
- Part of
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- Journal:
- Proceedings of the Edinburgh Mathematical Society / Volume 55 / Issue 1 / February 2012
- Published online by Cambridge University Press:
- 20 June 2011, pp. 23-51
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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.
and 
. They correspond to 
and 
-module structures. We establish that the transition matrices relating these two bases are unitriangular with coefficients in ℕ[