Quantum integrability and generalised quantum Schubert calculus
| Autor: | Christian Korff, Vassily Gorbounov |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: |
Quantum t-design
General Mathematics Schubert calculus FOS: Physical sciences 01 natural sciences Mathematics - Algebraic Geometry Quantum probability Mathematics - Quantum Algebra 0103 physical sciences Quantum operation Quantum no-deleting theorem FOS: Mathematics Quantum Algebra (math.QA) 0101 mathematics Representation Theory (math.RT) Quantum statistical mechanics Algebraic Geometry (math.AG) 14M15 14F43 55N20 55N22 05E05 82B23 19L47 Mathematics Quantum geometry Nonlinear Sciences - Exactly Solvable and Integrable Systems 010102 general mathematics K-Theory and Homology (math.KT) Algebra Mathematics - K-Theory and Homology Quantum algorithm 010307 mathematical physics Exactly Solvable and Integrable Systems (nlin.SI) Mathematics - Representation Theory |
| Zdroj: | Advances in Mathematics |
| ISSN: | 0001-8708 |
| Popis: | 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. Comment: 57 pages, 10 figures; v2: some references added and some minor changes; v3: abstract shortened, some typos corrected and a discussion of the Bethe roots for the non-equivariant case added; v4: accepted version |
| Databáze: | OpenAIRE |
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