Rational semistandard tableaux and character formula for the Lie superalgebra $\hat{\frak{gl}}_{\infty|\infty}$

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dc.creatorKwon, Jae-Hoon
dc.date2006-04-29
dc.date.accessioned2026-07-07T07:13:47Z
dc.date.available2026-07-07T07:13:47Z
dc.descriptionA new combinatorial interpretation of the Howe dual pair $(\hat{\frak{gl}}_{\infty|\infty},\frak{gl}_n)$ acting on an infinite dimensional Fock space $\frak{F}^n$ of level $n$ is presented. The character of a quasi-finite irreducible highest weight representation of $\hat{\frak{gl}}_{\infty|\infty}$ occurring in $\frak{F}^n$ 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 $\frak{gl}_n$. This result also explains other Howe dual pairs including $\frak{gl}_n$.
dc.description39pages
dc.identifierhttps://arxiv.org/abs/math/0605005
dc.identifierhttp://arxiv.org/abs/math/0605005
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/112601
dc.subjectRepresentation Theory
dc.subject17B10; 05E10
dc.titleRational semistandard tableaux and character formula for the Lie superalgebra $\hat{\frak{gl}}_{\infty|\infty}$
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