Classification of simple modules over degenerate double Affine Hecke algebras of type A

Details Classification of simple modules over degenerate double Affine Hecke algebras of type A Classification of simple modules over degenerate double Affine Hecke algebras of type A

2003-04-29

arxiv.org/abs/math/0304474v1

Mathematics

Quantum Algebra

25pages, AMSLaTex

Scientific paper

We study a class of representations over the degenerate double affine Hecke algebra of gl_n by an algebraic method. As fundamental objects in this class, we introduce certain induced modules and study some of their properties. In particular, it is shown that these induced modules have unique simple quotient modules under certain conditions. Moreover, we show that any simple module in this class is obtained as such a simple quotient, and give a classification of all the simple modules.

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