A link between two elliptic quantum groups

1998/01/23 by Pavel Etingof, Olivier Schiffmann, Etingof, Pavel +1
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #math.QA

paper · pdf · doi:10.48550/arxiv.math/9801108

12 pages, Latex

arxiv created 1998/01/23 · openalex publication_date 1998/01/23 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct a fully faithful functor from the category C_F of finite-dimensional representations of Felder's (dynamical) elliptic quantum group E_tau,gamma(gl(n)) to a cretain category D_B of (infinite-dimensional) representations of Belavin's quantum elliptic algebra B by difference operators, and a fully faithful functor from the category C_B of finite-dimensional representations of B to D_B. As a corollary, we show that the abelian subcategories of C_B and C_F generated by tensor products of vector representations are equivalent.

Related

• On the quantum Kazhdan-Lusztig functor
• Elliptic Quantum Groups U_q,p(gl_N) and E_q,p(gl_N)
• Elliptic quantum groups and their finite-dimensional representations
• Elliptic Central Characters and Blocks of Finite Dimensional Representations of Quantum Affine Algebras
• Elliptic Stable Envelopes and Finite-dimensional Representations of Elliptic Quantum Group