• 제목/요약/키워드: rational Cherednik algebra

검색결과 2건 처리시간 0.021초

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

  • Shin, Gicheol
    • 호남수학학술지
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    • 제41권2호
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    • pp.421-433
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    • 2019
  • 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.

A NOTE ON g-SEMISIMPLICITY OF A FINITE-DIMENSIONAL MODULE OVER THE RATIONAL CHEREDNIK ALGEBRA OF TYPE A

  • Gicheol Shin
    • 충청수학회지
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    • 제36권2호
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    • pp.77-86
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    • 2023
  • The purpose of this paper is to show that a certain finite dimensional representation of the rational Cherednik algebra of type A has a basis consisting of simultaneous eigenvectors for the actions of a certain family of commuting elements, which are introduced in the author's previous paper. To this end, we introduce a combinatorial object, which is called a restricted arrangement of colored beads, and consider an action of the affine symmetric group on the set of the arrangements.