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

Ryan Kinser; Allen Knutson; Jenna Rajchgot

doi:10.1215/00127094-2018-0043

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.

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Ryan Kinser. Allen Knutson. Jenna Rajchgot. "Three combinatorial formulas for type $A$ quiver polynomials and $K$ -polynomials." Duke Math. J. 168 (4) 505 - 551, 15 March 2019. https://doi.org/10.1215/00127094-2018-0043

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Received: 19 March 2015; Revised: 12 July 2018; Published: 15 March 2019

First available in Project Euclid: 4 February 2019

zbMATH: 07055150

MathSciNet: MR3916063

Digital Object Identifier: 10.1215/00127094-2018-0043

Subjects:

Primary: 14M12

Secondary: 05E15 , 14C17 , 19E08

Keywords: degeneracy locus , K-polynomial , lacing diagram , matrix Schubert variety , multidegree , orbit closure , pipe dream , quiver locus , representation variety

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