Quantum Integrability and Generalised Quantum Schubert Calculus

Vasily Gorbunov; Christian Korff

doi:10.1016/j.aim.2017.03.030

Quantum Integrability and Generalised Quantum Schubert Calculus

Vasily Gorbunov, Christian Korff

Mathematical Science

University of Glasgow

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

30 Citations (Scopus)

11 Downloads (Pure)

Abstract

We introduce and study a new mathematical structure in the generalised (quantum) cohomology theory for Grassmannians. Namely, we relate the Schubert calculus to a quantum integrable system known in the physics literature as the asymmetric six-vertex model. Our approach offers a new perspective on already established and well-studied special cases, for example equivariant K-theory, and in addition allows us to formulate a conjecture on the so-far unknown case of quantum equivariant K-theory.

Original language	English
Pages (from-to)	282-356
Number of pages	75
Journal	Advances in Mathematics
Volume	313
Early online date	16 May 2017
DOIs	https://doi.org/10.1016/j.aim.2017.03.030
Publication status	Published - 20 Jun 2017

Bibliographical note

Acknowledgments
The authors would like to thank the Max Planck Institute for Mathematics Bonn, where part of this work was carried out, for hospitality. They are grateful to Leonardo Mihalcea and Alexander Varchenko for comments on a draft version of the article. C. K. also gratefully acknowledges discussions with Gwyn Bellamy, Christian Voigt, Paul Zinn-Justin and would like to thank the organisers Anita Ponsaing and Paul Zinn-Justin for their kind invitation to the workshop Combinatorics and Integrability, Presqu'île de Giens, 23–27 June 2014, where the results of this article were presented.

Keywords

Quantum cohomology
Quantum K-theory
Enumerative combinatorics
Exactly solvable models
Bethe ansatz

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Accepted Manuscript
© 2017. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
Accepted author manuscript, 1.91 MBLicence: CC BY-NC-ND

Cite this

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abstract = "We introduce and study a new mathematical structure in the generalised (quantum) cohomology theory for Grassmannians. Namely, we relate the Schubert calculus to a quantum integrable system known in the physics literature as the asymmetric six-vertex model. Our approach offers a new perspective on already established and well-studied special cases, for example equivariant K-theory, and in addition allows us to formulate a conjecture on the so-far unknown case of quantum equivariant K-theory.",

keywords = "Quantum cohomology , Quantum K-theory , Enumerative combinatorics , Exactly solvable models , Bethe ansatz ",

author = "Vasily Gorbunov and Christian Korff",

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KW - Quantum cohomology

KW - Quantum K-theory

KW - Enumerative combinatorics

KW - Exactly solvable models

KW - Bethe ansatz

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DO - 10.1016/j.aim.2017.03.030

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JF - Advances in Mathematics

ER -

Quantum Integrability and Generalised Quantum Schubert Calculus

Abstract

Bibliographical note

Keywords

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