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The -orbit of , Kostant's formula for powers of the Euler product and affine Weyl groups as permutations of Z
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Denominator identities and Lie superalgebras (extended abstract)
No full textWe provide formulas for the Weyl-Kac denominator and superdenominator of a basic classical Lie superalgebra for a distinguished set of positive roots. © 2010 Discrete Mathematics and Theoretical Computer Science (DMTCS), Nancy, France
ABELIAN SUBALGEBRAS OF Z_2-GRADED LIE ALGEBRAS AND AFFINE WEYL GROUP
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Corrigendum to “Multiplets of representations, twisted Dirac operators and Vogan's conjecture in affine setting” (Multiplets of representations, twisted Dirac operators and Vogan's conjecture in affine setting (2008) 217(6) (2485–2562), (S0001870807003088), (10.1016/j.aim.2007.10.005))
No full textConformal embeddings in affine vertex superalgebras
Full text linkThis paper is a natural continuation of our previous work on conformal embeddings of vertex algebras [6], [7], [8]. Here we consider conformal embeddings in simple affine vertex superalgebra Vk(g) where g=g0 ̄⊕g1 ̄ is a basic classical simple Lie superalgebra. Let Vk(g0 ̄) be the subalgebra of Vk(g) generated by g0 ̄. We first classify all levels k for which the embedding Vk(g0 ̄) in Vk(g) is conformal. Next we prove that, for a large family of such conformal levels, Vk(g) is a completely reducible Vk(g0 ̄)–module and obtain decomposition rules. Proofs are based on fusion rules arguments and on the representation theory of certain affine vertex algebras. The most interesting case is the decomposition of V−2(osp(2n+8|2n)) as a finite, non simple current extension of V−2(Dn+4)⊗V1(Cn). This decomposition uses our previous work [10] on the representation theory of V−2(Dn+4). We also study conformal embeddings gl(n|m)↪sl(n+1|m) and in most cases we obtain decomposition rules
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