On the spectrum of exterior algebra, and generalized exponents of small representations

We present some results about the irreducible representations appearing in the exterior algebra Λ g , where g is a simple Lie algebra over C . For Lie algebras of type B , C or D we prove that certain irreducible representations, associated to weights characterized in a combinatorial way, appear as...

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Veröffentlicht in:Bollettino della Unione matematica italiana (2008) 2024-06, Vol.17 (2), p.283-312
1. Verfasser: Di Trani, Sabino
Format: Artikel
Sprache:eng
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Zusammenfassung:We present some results about the irreducible representations appearing in the exterior algebra Λ g , where g is a simple Lie algebra over C . For Lie algebras of type B , C or D we prove that certain irreducible representations, associated to weights characterized in a combinatorial way, appear as irreducible components of Λ g . Moreover, we propose an analogue of a conjecture of Kostant, about irreducibles appearing in the exterior algebra of the little adjoint representation. Finally, we give some closed expressions, in type B , C and D , for generalized exponents of small representations that are fundamental representations and we propose a generalization of some results of De Concini, Möseneder Frajria, Procesi and Papi about the module of special covariants of adjoint and little adjoint type.
ISSN:1972-6724
2198-2759
DOI:10.1007/s40574-023-00390-8