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Effective constructions in plethysms and Weintraub’s conjecture. (English) Zbl 1292.05264

Summary: We give a short proof of Weintraub’s conjecture [S. Weintraub, J. Algebra 129, No. 1, 103–114 (1990; Zbl 0695.20013)], first proved in [P. Bürgisser et al., J. Algebra 328, No. 1, 322–329 (2011; Zbl 1241.20050)], by constructing explicit highest weight vectors in the plethysms \(S^p(\wedge^{2q}W)\).

MSC:

05E10 Combinatorial aspects of representation theory
05E05 Symmetric functions and generalizations
20C30 Representations of finite symmetric groups
22E46 Semisimple Lie groups and their representations
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