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Tr. Mosk. Mat. Obs., 2017, Volume 78, Issue 2, Pages 311–330 (Mi mmo602)  

On some modules of covariants for a reflection group

C. De Concini, P. Papi

Dipartimento di Matematica, Sapienza Università di Roma, Italy

Abstract: Let $\mathfrak g$ be a simple Lie algebra with Cartan subalgebra $\mathfrak{h}$ and Weyl group $W$. We build up a graded isomorphism $\smash{(\bigwedge\mathfrak{h}\otimes\mathcal H\otimes \mathfrak{h})\vphantom)^W}\to (\bigwedge \mathfrak{g}\otimes \mathfrak{g})^\mathfrak{g}$ of $(\bigwedge \mathfrak{g})^\mathfrak{g}\cong S(\mathfrak{h})^W$-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.

Key words and phrases: exterior algebra, covariants, small representation, Dunkl operators

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English version:
Transactions of the Moscow Mathematical Society, 2017, 78, 257–273

Document Type: Article
UDC: 512.813.4, 512.817.72
MSC: 117B20
Received: 01.06.2017
Revised: 01.07.2017
Language: English

Citation: C. De Concini, P. Papi, “On some modules of covariants for a reflection group”, Tr. Mosk. Mat. Obs., 78, no. 2, MCCME, M., 2017, 311–330; Trans. Moscow Math. Soc., 78 (2017), 257–273

Citation in format AMSBIB
\Bibitem{ConPap17}
\by C.~De~Concini, P.~Papi
\paper On some modules of covariants for a~reflection group
\serial Tr. Mosk. Mat. Obs.
\yr 2017
\vol 78
\issue 2
\pages 311--330
\publ MCCME
\publaddr M.
\mathnet{http://mi.mathnet.ru/mmo602}
\elib{http://elibrary.ru/item.asp?id=37045069}
\transl
\jour Trans. Moscow Math. Soc.
\yr 2017
\vol 78
\pages 257--273
\crossref{https://doi.org/10.1090/mosc/272}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85037656107}


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