Quantum Integrability and Generalised Quantum Schubert Calculus

Vasily Gorbunov, Christian Korff

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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.
Original languageEnglish
Pages (from-to)282-356
Number of pages75
JournalAdvances in Mathematics
Volume313
Early online date16 May 2017
DOIs
Publication statusPublished - 20 Jun 2017

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Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)

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