Resumen de Decomposition ofq-deformed Fock spaces
Masaki Kashiwara, T. Miwa, E. Stern
A decomposition of the level-oneq-deformed Fock space representations ofU q(sl n ) is given. It is found that the action ofU′ q(sl n ) on these Fock spaces is centralized by a Heisenberg algebra, which arises from the center of the affine Hecke algebraĤ N in the limitN → ∞. Theq-deformed Fock space is shown to be isomorphic as aU′ q(sl n )-Heisenberg-bimodule to the tensor product of a level-one irreducible highest weight representation ofU′ q(sl n ) and the Fock representation of the Heisenberg algebra. The isomorphism is used to decompose theq-wedging operators, which are intertwiners between theq-deformed Fock spaces, into constituents coming fromU′ q(sl n ) and from the Heisenberg algebra.
