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Kostka-Shoji Polynomials and Lusztig's Convolution Diagram
by Michael Finkelberg   Andrei Ionov

Vol. 13 No. 1 (2018) P.31~P.42
 DOI: https://doi.org/10.21915/BIMAS.2018102 10.21915/BIMAS.2018102

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 (for regular $\mu$, and conjecturally for arbitrary $\mu$) 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 $\tilde{A}_{r-1}$.

KEYWORDS
Kostka-Shoji polynomials, cyclic quiver, convolution diagram, Frobenius splitting, affine flag variety, Bott-Samelson-Demazure-Hansen resolution.

MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 05E15 (14M15, 13A35).

MILESTONES