Duke Mathematical Journal

Three combinatorial formulas for type $A$ quiver polynomials and $K$-polynomials

Abstract

We provide combinatorial formulas for the multidegree and $K$-polynomial of an arbitrarily oriented type $A$ quiver locus. These formulas are generalizations of three formulas by Knutson, Miller, and Shimozono from the equioriented setting. In particular, we prove the $K$-theoretic component formula conjectured by Buch and Rimányi.

Article information

Source
Duke Math. J., Volume 168, Number 4 (2019), 505-551.

Dates
Revised: 12 July 2018
First available in Project Euclid: 4 February 2019

https://projecteuclid.org/euclid.dmj/1549270814

Digital Object Identifier
doi:10.1215/00127094-2018-0043

Mathematical Reviews number (MathSciNet)
MR3916063

Zentralblatt MATH identifier
07055150

Citation

Kinser, Ryan; Knutson, Allen; Rajchgot, Jenna. Three combinatorial formulas for type $A$ quiver polynomials and $K$ -polynomials. Duke Math. J. 168 (2019), no. 4, 505--551. doi:10.1215/00127094-2018-0043. https://projecteuclid.org/euclid.dmj/1549270814

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