On some modules of covariants for a reflection group

2017/06/01 by De Concini, Corrado, Papi, Paolo
#FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1706.00189

Abstract

Let \mathfrak g be a simple Lie algebra with Cartan subalgebra \mathfrak h and Weyl group W. We build up a graded map (\mathcal H⊗ \bigwedge\mathfrak h⊗ \mathfrak h)^W→ (\bigwedge \mathfrak g⊗ \mathfrak g)^\mathfrak g of (\bigwedge \mathfrak g)^\mathfrak g≅ 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. New version with different title. Various improvements. New section 7.

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