학술저널
A NOTE ON g-SEMISIMPLICITY OF A FINITE-DIMENSIONAL MODULE OVER THE RATIONAL CHEREDNIK ALGEBRA OF TYPE A
A NOTE ON g-SEMISIMPLICITY OF A FINITE-DIMENSIONAL MODULE OVER THE RATIONAL CHEREDNIK ALGEBRA OF TYPE A
- 충청수학회
- Journal of the Chungcheong Mathematical Society
- Volume 36, No. 2
-
2023.0577 - 86 (10 pages)
-
DOI : 10.14403/jcms.2023.36.2.77
- 5
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.
1. Introduction
2. Restriced arrangements of colored beads
3. Rational Cherednik algebra
4. Main theorem: g-semisimplicity
References
(0)
(0)