Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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A NOTE ON g-SEMISIMPLICITY OF A FINITE-DIMENSIONAL MODULE OVER THE RATIONAL CHEREDNIK ALGEBRA OF TYPE A

  • Gicheol Shin (Department of Mathematics Education Seowon University)
  • Received : 2023.01.09
  • Accepted : 2023.03.28
  • Published : 2023.05.30
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Abstract

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.

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References

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