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

2003/04/29 by Takeshi Suzuki, Suzuki, Takeshi
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT) #math.QA #math.RT

paper · pdf · doi:10.48550/arxiv.math/0304474

25pages, AMSLaTex

arxiv created 2003/04/29 · openalex publication_date 2003/04/29 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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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