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 |
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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. |
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ISSN: | 1972-6724 2198-2759 |
DOI: | 10.1007/s40574-023-00390-8 |