Skew Schur Polynomials and Cyclic Sieving Phenomenon

초록

Let k and m be positive integers and lambda/mu a skew partition. We compute the prin-cipal specialization of the skew Schur polynomials s lambda/mu (x1, ... , xk) modulo qm - 1 under suitable conditions. We interpret the results thus obtained from the viewpoint of the cyclic sieving phenomenon on semistandard Young skew tableaux of shape lambda/mu. As an application, we deal with evaluations of the principal specialization of the skew Schur polynomials at roots of unity.