Reeder’s Conjecture for Even Orthogonal Lie Algebras

Trani, Sabino Di

doi:10.1007/s10468-022-10115-8

Algebr Represent Theor

2022

DOI: 10.1007/s10468-022-10115-8

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Reeder’s Conjecture for Even Orthogonal Lie Algebras

Sabino Di Trani

Abstract: In the paper we complete a case by case proof of Reeder’s Conjecture started in our previous work, proving the conjecture for simple Lie algebras of type D and for the exceptional cases.

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2023

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

Di Trani

2023

Boll Unione Mat Ital

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We present some results about the irreducible representations appearing in the exterior algebra $$\Lambda \mathfrak {g}$$ Λ g , where $$\mathfrak {g}$$ g is a simple Lie algebra over $${\mathbb {C}}$$ 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 $$\Lambda \mathfrak {g}$$ 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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On the spectrum of exterior algebra, and generalized exponents of small representations

Di Trani

2023

Boll Unione Mat Ital

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Reeder’s Conjecture for Even Orthogonal Lie Algebras

Abstract: In the paper we complete a case by case proof of Reeder’s Conjecture started in our previous work, proving the conjecture for simple Lie algebras of type D and for the exceptional cases.

Cited by 1 publication

References 18 publications

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

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

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