Remote Access Transactions of the Moscow Mathematical Society

Transactions of the Moscow Mathematical Society

ISSN 1547-738X(online) ISSN 0077-1554(print)

   
 
 

 

On some modules of covariants for a reflection group


Authors: C. De Concini and P. Papi
Original publication: Trudy Moskovskogo Matematicheskogo Obshchestva, tom 78 (2017), vypusk 2.
Journal: Trans. Moscow Math. Soc. 2017, 257-273
DOI: https://doi.org/10.1090/mosc/272
Published electronically: December 1, 2017
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Abstract | References | Additional Information

Abstract: Let $ \mathfrak{g}$ be a simple Lie algebra with Cartan subalgebra $ \mathfrak{h}$ and Weyl group $ W$. We build up a graded isomorphism $ \smash {\bigl (\bigwedge \mathfrak{h}\otimes \mathcal H\otimes \mathfrak{h}\bi... ... )^W}\to \bigl (\bigwedge \mathfrak{g}\otimes \mathfrak{g}\big )^{\mathfrak{g}}$ of $ \bigl (\bigwedge \mathfrak{g}\big )^{\mathfrak{g}}\cong S(\mathfrak{h})^W$-modules, where $ \mathcal H$ is the space of $ W$-harmonics. In this way we prove an enhanced form of a conjecture of Reeder for the adjoint representation.


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Additional Information

C. De Concini
Affiliation: Dipartimento di Matematica, Sapienza Università di Roma, Italy
Email: deconcin@mat.uniroma1.it

P. Papi
Affiliation: Dipartimento di Matematica, Sapienza Università di Roma, Italy
Email: papi@mat.uniroma1.it

DOI: https://doi.org/10.1090/mosc/272
Keywords: Exterior algebra, covariants, small representation, Dunkl operators
Published electronically: December 1, 2017
Dedicated: To Ernest Vinberg on the occasion of his 80th birthday
Article copyright: © Copyright 2017 C. De Concini, P.Papi

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