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

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-sln(c) of type sl(n), which are analogous to the Dunkl-Cherednik elements of the rational Cherednik algebra H-gln(c) of type gl(n). We also introduce the raising and lowering element of H-sln(c) which are useful in the representation theory of the algebra H-sln(c), and provide simple results related to these elements.