Quantum Integrability and Generalised Quantum Schubert Calculus

Vasily Gorbunov, Christian Korff

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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 languageEnglish
Pages (from-to)282-356
Number of pages75
JournalAdvances in Mathematics
Early online date16 May 2017
Publication statusPublished - 20 Jun 2017

Bibliographical note

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.


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


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