Rational semistandard tableaux and character formula for the Lie superalgebra

A new combinatorial interpretation of the Howe dual pair acting on an infinite-dimensional Fock space is presented. The character of a quasi-finite irreducible highest weight representation of 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 gln. This result also explains other Howe dual pairs (g,gln), where g is a Lie superalgebra.