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Representations for Lie superalgebras of type C

✍ Scribed by Chanyoung Lee Shader

Publisher: Elsevier Science
Year: 2002
Tongue: English
Weight: 152 KB
Volume: 255
Category: Article
ISSN: 0021-8693
DOI: 10.1016/s0021-8693(02)00152-7

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✦ Synopsis

Let G = osp(2, 2n) be the classical Lie superalgebra of type C of rank n + 1. Let λ be a partition with λ 1 n. Then λ labels a finite-dimensional irreducible G-module, V (λ). We describe the character of V (λ) in terms of tableaux. This tableaux description of characters enable us to decompose T = f V , the f -fold tensor product of the natural representation of G, into its irreducible submodules and to show that the centralizer algebra of G on T is isomorphic to the Brauer algebra B f (2 -2n) for n > f .

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