Infinite-dimensional representations of U_q(\mathfraksl₂) and the shadow world: quantum 6j-symbols for Verma modules

2024/10/24 by Solovyev, Dmitry
#FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2410.18463

Abstract

This paper initiates the study of invariants of links associated to infinite-dimensional representations of U_q(\mathfraksl₂) using graphical representation for quantum 6j-symbols, the shadow world. We obtain formulae for q3j-symbols and q6j-symbols for Verma modules and study their properties. This hints at the structure of the possible target category for Reshetikhin-Turaev functor for such an invariant.

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