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Tensor products of fundamental representations. (English) Zbl 0661.20031
Let G be a reductive algebraic group over a field of characteristic 0, T a maximal torus of G, and B a Borel subgroup of G containing T. Corresponding to each dominant weight X with respect to T, B there is an irreducible representation V(X) of G with highest weight X. The aim of this paper is to compute the tensor product decomposition \(V(X_ 1)\otimes V(X_ 2)=\otimes m_{\psi}V(\psi)\), where \(X_ 1\), \(X_ 2\) are fundamental weights. Explicit results are given for the general linear, symplectic and orthogonal groups.
The calculations are based on two previous papers of the first author [Am. J. Math. 109, 395-400 (1987; Zbl 0634.20016); ibid. 109, 401-415 (1987; Zbl 0634.20017)].
Reviewer: B.Srinivasan

20G05 Representation theory for linear algebraic groups
20G15 Linear algebraic groups over arbitrary fields
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