Kostka-Shoji polynomials and Lusztig's convolution diagram

Abstract

We propose an $r$-variable version of Kostka-Shoji polynomials $K_{\lambda \mu }^{-}$ for $r$-multipartitions $\lambda ,\mu$. Our version has positive integral coefficients and encodes the graded multiplicities in the space of global sections of a line bundle over Lusztig's iterated convolution diagram for the cyclic quiver ${\tilde{A}}_{r-1}$.

arXiv commentv3: references updated