Equivariant $K$-theory of Grassmannians II: the Knutson-Vakil conjecture

Oliver Pechenik; Alexander Yong

doi:10.1112/S0010437X16008186

Equivariant $K$-theory of Grassmannians II: the Knutson-Vakil conjecture

Oliver Pechenik
, Alexander Yong

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

In 2005, Knutson-Vakil conjectured a puzzle rule for equivariant -theory of Grassmannians. We resolve this conjecture. After giving a correction, we establish a modified rule by combinatorially connecting it to the authors' recently proved tableau rule for the same Schubert calculus problem.

Original language	English (US)
Pages (from-to)	667-677
Number of pages	11
Journal	Compositio Mathematica
Volume	153
Issue number	4
DOIs	https://doi.org/10.1112/S0010437X16008186
State	Published - Apr 1 2017

Keywords

Grassmannian
Littlewood-Richardson rule
Schubert calculus
equivariant K-theory
puzzle

ASJC Scopus subject areas

Algebra and Number Theory

Online availability

10.1112/S0010437X16008186

http://dx.doi.org/10.1112/S0010437X16008186

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title = "Equivariant \$K\$-theory of Grassmannians II: the Knutson-Vakil conjecture",

abstract = "In 2005, Knutson-Vakil conjectured a puzzle rule for equivariant -theory of Grassmannians. We resolve this conjecture. After giving a correction, we establish a modified rule by combinatorially connecting it to the authors' recently proved tableau rule for the same Schubert calculus problem.",

keywords = "Grassmannian, Littlewood-Richardson rule, Schubert calculus, equivariant K-theory, puzzle",

author = "Oliver Pechenik and Alexander Yong",

note = "We thank Hugh Thomas for enlightening conversations during our work on [PY15] and also thank Allen Knutson and Ravi Vakil for helpful correspondence. We thank two anonymous reviewers for helpful comments. O. P. was supported by an Illinois Distinguished Fellowship, an NSF Graduate Research Fellowship and NSF MCTP grant DMS 0838434. A. Y. was supported by NSF grants.",

year = "2017",

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journal = "Compositio Mathematica",

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AU - Pechenik, Oliver

AU - Yong, Alexander

N1 - We thank Hugh Thomas for enlightening conversations during our work on [PY15] and also thank Allen Knutson and Ravi Vakil for helpful correspondence. We thank two anonymous reviewers for helpful comments. O. P. was supported by an Illinois Distinguished Fellowship, an NSF Graduate Research Fellowship and NSF MCTP grant DMS 0838434. A. Y. was supported by NSF grants.

PY - 2017/4/1

Y1 - 2017/4/1

N2 - In 2005, Knutson-Vakil conjectured a puzzle rule for equivariant -theory of Grassmannians. We resolve this conjecture. After giving a correction, we establish a modified rule by combinatorially connecting it to the authors' recently proved tableau rule for the same Schubert calculus problem.

AB - In 2005, Knutson-Vakil conjectured a puzzle rule for equivariant -theory of Grassmannians. We resolve this conjecture. After giving a correction, we establish a modified rule by combinatorially connecting it to the authors' recently proved tableau rule for the same Schubert calculus problem.

KW - Grassmannian

KW - Littlewood-Richardson rule

KW - Schubert calculus

KW - equivariant K-theory

KW - puzzle

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UR - https://www.scopus.com/pages/publications/85040789258#tab=citedBy

U2 - 10.1112/S0010437X16008186

DO - 10.1112/S0010437X16008186

M3 - Article

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VL - 153

SP - 667

EP - 677

JO - Compositio Mathematica

JF - Compositio Mathematica

IS - 4

ER -

Equivariant $K$-theory of Grassmannians II: the Knutson-Vakil conjecture

Abstract

Keywords

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