Towards a combinatorial representation theory for the rational Cherednik algebra of type G(r,p,n)

Details Towards a combinatorial representation theory for the rational Cherednik algebra of type G(r,p,n) Towards a combinatorial representation theory for the rational Cherednik algebra of type G(r,p,n)

2006-12-23

arxiv.org/abs/math/0612733v3

Mathematics

Representation Theory

20 pages; in the 3rd version we have omitted some well-known material to make the paper shorter and included a proof of the an

Scientific paper

The goal of this paper is to lay the foundations for a combinatorial study, via orthogonal functions and intertwining operators, of category O for the rational Cherednik algebra of type G(r,p,n). As a first application, we give a self-contained and elementary proof of the analog for the groups G(r,p,n), with r>1, of Gordon's theorem (previously Haiman's conjecture) on the diagonal coinvariant ring. We impose no restriction on p; the result for p

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