Higher cohomology vanishing of line bundles on generalized Springer's resolution

Abstract

We give a proof of a conjecture raised by Michael Finkelberg and Andrei Ionov. As a corollary, the coefficients of multivariable version of Kostka functions introduced by Finkelberg and Ionov are non-negative.

A new section added with arguments on quiver Kostka-Shoji polynomials (after D. Orr and M. Shimozono) for cyclic and ADE types