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• W2434896206 abstract "We study affine fusion with the adjoint representation. For simple Lie algebras, elementary and universal formulas determine the decomposition of a tensor product of an integrable highest-weight representation with the adjoint representation. Using the (refined) affine depth rule, we prove that equally striking results apply to adjoint affine fusion. For diagonal fusion, a coefficient equals the number of nonzero Dynkin labels of the relevant affine highest weight, minus 1. A nice lattice-polytope interpretation follows and allows the straightforward calculation of the genus-1 1-point adjoint Verlinde dimension, the adjoint affine fusion tadpole. Explicit formulas, (piecewise) polynomial in the level, are written for the adjoint tadpoles of all classical Lie algebras. We show that off-diagonal adjoint affine fusion is obtained from the corresponding tensor product by simply dropping non-dominant representations." @default.
• W2434896206 created "2016-06-24" @default.
• W2434896206 creator A5015704880 @default.
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• W2434896206 date "2016-06-01" @default.
• W2434896206 modified "2023-10-03" @default.
• W2434896206 title "Adjoint affine fusion and tadpoles" @default.
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• W2434896206 doi "https://doi.org/10.1063/1.4954909" @default.
• W2434896206 hasPublicationYear "2016" @default.
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