Baxter Q-operator from quantum K-theory
| Autor: | Anton M. Zeitlin, Andrey Smirnov, Petr P. Pushkar |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2016 |
| Předmět: |
High Energy Physics - Theory
General Mathematics FOS: Physical sciences 01 natural sciences Mathematics - Algebraic Geometry Mathematics::Algebraic Geometry 0103 physical sciences FOS: Mathematics Quantum operation Tautological one-form Representation Theory (math.RT) 0101 mathematics Algebraic Geometry (math.AG) Mathematics::Symplectic Geometry Mathematical Physics Mathematics Mathematical physics Quantum group 010102 general mathematics Spectrum (functional analysis) K-Theory and Homology (math.KT) Mathematical Physics (math-ph) Tautological line bundle Algebra Ladder operator High Energy Physics - Theory (hep-th) Mathematics - K-Theory and Homology Quantum algorithm 010307 mathematical physics Exchange operator Mathematics - Representation Theory |
| Popis: | We define and study the quantum equivariant $K$-theory of cotangent bundles over Grassmannians. For every tautological bundle in the $K$-theory we define its one-parametric deformation, referred to as quantum tautological bundle. We prove that the spectrum of operators of quantum multiplication by these quantum classes is governed by the Bethe ansatz equations for the inhomogeneous $XXZ$ spin chain. In addition, we prove that each such operator corresponds to the universal elements of quantum group $\mathcal{U}_{\hbar}(\widehat{\mathfrak{sl}}_2)$. In particular, we identify the Baxter operator for the $XXZ$ spin chain with the operator of quantum multiplication by the exterior algebra tautological bundle. The explicit universal combinatorial formula for this operator is found. The relation between quantum line bundles and quantum dynamical Weyl group is shown. v4: 57 pages, major revision |
| Databáze: | OpenAIRE |
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