Rational semistandard tableaux and character formula for the Lie superalgebra \frakgl_∞|∞

2006/04/29 by Kwon, Jae-Hoon
#05E10 #17B10 #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.math/0605005

Abstract

A new combinatorial interpretation of the Howe dual pair (\frakgl_∞|∞,\frakgl_n) acting on an infinite dimensional Fock space \frakFⁿ of level n is presented. The character of a quasi-finite irreducible highest weight representation of \frakgl_∞|∞ occurring in \frakFⁿ is realized in terms of certain bitableaux of skew shapes. We study a general combinatorics of these bitableaux, including Robinson-Schensted-Knuth correspondence and Littlewood-Richardson rule, and then its dual relation with the rational semistandard tableaux for \frakgl_n. This result also explains other Howe dual pairs including \frakgl_n.

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