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15 March 2019 Three combinatorial formulas for type A quiver polynomials and K-polynomials
Ryan Kinser, Allen Knutson, Jenna Rajchgot
Duke Math. J. 168(4): 505-551 (15 March 2019). 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

Information

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

Rights: Copyright © 2019 Duke University Press

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Vol.168 • No. 4 • 15 March 2019
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