Representations of the Dynamical Affine Quantum Group U_q,x(\widehatsl₂)=U_q,λ(\widehatsl₂) and Hypergeometric Functions

2014/05/30 by Bharath Narayanan, Narayanan, Bharath
Mathematics · #17B37 #81R10 #FOS: Mathematics #Number Theory (math.NT) #Quantum Algebra (math.QA) #Representation Theory (math.RT) #math.NT #math.QA #math.RT #msc:17B37 #msc:81R10

paper · pdf · doi:10.48550/arxiv.1405.7853

38 pages, 2 figures. Misprints corrected and some improvements added

arxiv created 2015/07/26 · arxiv updated 2015/07/28

Abstract

The representation theory of the Hopf algebroid U_q,x(\widehatsl₂)=U_q,λ(\widehatsl₂) is initiated and it is established that the intertwiner between the tensor products of dynamical evaluation modules is a well-poised balanced ₁₀W₉ symbol, confirming a conjecture of Konno, that the degeneration of the elliptic ₁₂V₁₁ series to ₁₀W₉ can be proven based on the representation theory of U_q,x(\widehatsl₂), the degeneration of the elliptic algebra U_q,p(\widehatsl₂) as p → 0.

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