Abstract
A new combinatorial interpretation of the Howe dual pair ( gl Ë â | â , gl n ) acting on an infinite-dimensional Fock space is presented. The character of a quasi-finite irreducible highest weight representation of gl Ë â | â occurring in the Fock space is realized in terms of certain bitableaux of skew shapes. We study a general combinatorics of these bitableaux, including the RobinsonâSchenstedâKnuth correspondence and the LittlewoodâRichardson rule, and then its dual relation with rational semistandard tableaux for gl n . This result also explains other Howe dual pairs ( g , gl n ) , where g is a Lie superalgebra.
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