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Irreducible Characters of General Linear Superalgebra and Super Duality

โœ Scribed by Shun-Jen Cheng; Ngau Lam


Publisher
Springer
Year
2010
Tongue
English
Weight
387 KB
Volume
298
Category
Article
ISSN
0010-3616

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Character formula for infinite-dimension
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The Fock space of m + p bosonic and n + q fermionic quantum oscillators forms a unitarizable module of the general linear superalgebra gl m+p| n+q . Its tensor powers decompose into direct sums of infinite-dimensional irreducible highest-weight gl m+p| n+q -modules. We obtain an explicit decompositi

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The structure of the Hopf superalgebra B of regular functions on the general linear supergroup is developed, and applied to study the representation theory of the supergroup. It is shown that the general linear supergroup can be reconstructed from B in a way reminiscent of the Tannaka-Krein theory.