Character and dimension formulae for general linear superalgebra

dc.creatorSu, Yucai
dc.creatorZhang, R. B.
dc.date2004-03-19
dc.date2004-05-18
dc.date.accessioned2026-07-07T05:06:32Z
dc.date.available2026-07-07T05:06:32Z
dc.descriptionThe generalized Kazhdan-Lusztig polynomials for the finite dimensional irreducible representations of the general linear superalgebra are computed explicitly. Using the result we establish a one to one correspondence between the set of composition factors of an arbitrary $r$-fold atypical $gl_{m|n}$-Kac-module and the set of composition factors of some $r$-fold atypical $gl_{r|r}$-Kac-module. The result of Kazhdan-Lusztig polynomials is also applied to prove a conjectural character formula put forward by van der Jeugt et al in the late 80s. We simplify this character formula to cast it into the Kac-Weyl form, and derive from it a closed formula for the dimension of any finite dimensional irreducible representation of the general linear superalgebra.
dc.description28 pages, re-writing results in terms of height vectors and adding one more result
dc.identifierhttps://arxiv.org/abs/math/0403315
dc.identifierhttp://arxiv.org/abs/math/0403315
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/70509
dc.subjectQuantum Algebra
dc.subjectRepresentation Theory
dc.subject17B10
dc.titleCharacter and dimension formulae for general linear superalgebra
dc.typetext

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