The Plancherel formula for complex semisimple quantum groups

2019/06/06 by Christian C. Voigt, Voigt, Christian, Robert Yuncken +1 · 1 citation
Mathematics · #20G42 #46L51 #46L65 #Advanced Algebra and Geometry #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #FOS: Mathematics #Operator Algebras (math.OA) #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1906.02672

openalex publication_date 2019/06/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We calculate the Plancherel formula for complex semisimple quantum groups, that is, Drinfeld doubles of q -deformations of compact semisimple Lie groups. As a consequence we obtain a concrete description of their associated reduced group C^* -algebras. The main ingredients in our proof are the Bernstein-Gelfand-Gelfand complex and the Hopf trace formula.

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