Calogero-Moser space and Kostka polynomials

Abstract

We consider the canonical map from the Calogero-Moser space to symmetric powers of the affine line, sending conjugacy classes of pairs of n × n-matrices to their eigenvalues. We show that the character of a natural ℂ*-action on the scheme-theoretic zero fiber of this map is given by Kostka polynomials. A similar result is proved for a cyclic version of the Calogero-Moser space. © 2002 Elsevier Science (USA).