Rational semistandard tableaux and character formula for the Lie superalgebra [formula omitted

Abstract

A new combinatorial interpretation of the Howe dual pair ( gl ˆ ∞ | ∞ , gl n ) acting on an infinite-dimensional Fock space is presented. The character of a quasi-finite irreducible highest weight representation of gl ˆ ∞ | ∞ 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 Robinson–Schensted–Knuth correspondence and the Littlewood–Richardson 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.