Elliptic quantum groups and Baxter relations

2017/06/30 by Huafeng Zhang
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Algebra over a field #Algebraic structures and combinatorial models #Analytic continuation #Construct (python library) #Continuation #Homotopy and Cohomology in Algebraic Topology #Quantum #Ring (chemistry) #math-ph #math.MP #math.QA #math.RT

paper · pdf · doi:10.2140/ant.2018.12.599

published as Alg. Number Th. 12 (2018) 599-647 · 39 pages, published version

openalex created_date 2017/06/30 · arxiv created 2018/03/11 · openalex publication_date 2018/06/12 · arxiv updated 2018/06/20 · openalex updated_date 2026/08/05

Abstract

We introduce a category [math] of modules over the elliptic quantum group of [math] with well-behaved [math] -character theory. We construct asymptotic modules as analytic continuation of a family of finite-dimensional modules, the Kirillov–Reshetikhin modules. In the Grothendieck ring of this category we prove two types of identities: Generalized Baxter relations in the spirit of Frenkel–Hernandez between finite-dimensional modules and asymptotic modules. Three-term Baxter TQ relations of infinite-dimensional modules.

Citations

• Integrable Structure of Conformal Field Theory III. The Yang-Baxter Relation
• Algebraic Bethe ansatz for the elliptic quantum group E,(sl) and its applications