Decomposition ofq-deformed Fock spaces

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 algebra_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.