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COMPONENTS OF V (ρ) ⊗ V (ρ)

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Abstract

Let ρ be half the sum of the positive roots of a root system. We prove that if ⋋ is a dominant weight, ⋋ ≤ 2ρ with respect to the dominance order, and d is a saturation factor for the complex Lie algebra associated to the root system, then the irreducible representation V (d⋋) appears in the tensor product V (dρ) ⊗ V (dρ).

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Authors and Affiliations

  1. Dipartimento di Matematica e Fisica, Università del Salento, 73047, Lecce, Italy

    ROCCO CHIRIVÌ

  2. Department of Mathematics, University of North Carolina, Chapel Hill, NC, 27599-3250, USA

    SHRAWAN KUMAR

  3. Dipartimento di Matematica, Università di Pisa, 56127, Pisa, Italy

    ANDREA MAFFEI

Authors
  1. ROCCO CHIRIVÌ
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  2. SHRAWAN KUMAR
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  3. ANDREA MAFFEI
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Correspondence to SHRAWAN KUMAR.

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CHIRIVÌ, R., KUMAR, S. & MAFFEI, A. COMPONENTS OF V (ρ) ⊗ V (ρ). Transformation Groups 22, 645–650 (2017). https://doi.org/10.1007/s00031-016-9375-8

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  • DOI: https://doi.org/10.1007/s00031-016-9375-8

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