Singular polynomials for the symmetric group and Krawtchouk polynomials
نویسنده
چکیده
A singular polynomial is one which is annihilated by all Dunkl operators for a certain parameter value. These polynomials were first studied by Dunkl, de Jeu and Opdam, (Trans. Amer. Math. Soc. 346 (1994), 237-256). This paper constructs a family of such polynomials associated to the irreducible representation (N − 2, 1, 1) of the symmetric group SN for odd N and parameter values − 1 2 ,− 3 2 ,− 5 2 , . . .. The method depends on the use of Krawtchouk polynomials to carry out a change of variables in a generating function involved in the construction of nonsymmetric Jack polynomials labeled by (m, n, 0, . . . , 0) , m ≥ n.
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