USEFUL OPERATORS ON REPRESENTATIONS OF THE RATIONAL CHEREDNIK ALGEBRA OF TYPE n

Let n denote an integer greater than 2 and let c denote a nonzero complex number. In this paper, we introduce a family of elements of the rational Cherednik algebra $H^{sl_n}(c)$ of type $sl_n$, which are analogous to the Dunkl-Cherednik elements of the rational Cherednik algebra $H^{gl_n}(c)$ of ty...

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Bibliographic Details
Published inHonam mathematical journal Vol. 41; no. 2; pp. 421 - 433
Main Author Shin, Gicheol
Format Journal Article
LanguageKorean
Published 2019
Subjects
Dunkl-Cherednik operators
representation theory
rational Cherednik algebra
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Summary:Let n denote an integer greater than 2 and let c denote a nonzero complex number. In this paper, we introduce a family of elements of the rational Cherednik algebra $H^{sl_n}(c)$ of type $sl_n$, which are analogous to the Dunkl-Cherednik elements of the rational Cherednik algebra $H^{gl_n}(c)$ of type $gl_n$. We also introduce the raising and lowering element of $H^{sl_n}(c)$ which are useful in the representation theory of the algebra $H^{sl_n}(c)$, and provide simple results related to these elements.
Bibliography:KISTI1.1003/JNL.JAKO201917971494366
ISSN:1225-293X