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arXiv · 0706.4308

Reducibility of the polynomial representation of the degenerate double affine Hecke algebra

Pavel Etingof
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Abstract

In this note we determine the values of parameters c for which the polynomial representation of the degenerate double affine Hecke algebra (DAHA), i.e. the trigonometric Cherednik algebra, is reducible. Namely, we show that c is a reducibility point for the polynomial representation of the trigonometric Cherednik algebra for a root system R if and only if it is a reducibility point for the rational Cherednik algebra for the Weyl group of some root subsystem R' of R of the same rank; such subsystems for any R are given by the well known Borel-de Siebenthal algorithm. This result has been proved by Cherednik using a case-by-case method.

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BibTeXRIS

Pavel Etingof. 2007-06-28. Reducibility of the polynomial representation of the degenerate double affine Hecke algebra. https://arxiv.org/abs/0706.4308

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