The Plancherel formula for complex semisimple quantum groups

DOI10.24033/asens.2535arXiv1906.02672MaRDI QIDQ6172421

Christian Voigt, Robert Yuncken

Publication date: 19 July 2023

Published in: Annales scientifiques de l'École Normale Supérieure (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1906.02672

zbMATH Keywords

Plancherel formulaquantum groupsBGG complex

Mathematics Subject Classification ID

Noncommutative measure and integration (46L51) Quantum groups (quantized function algebras) and their representations (20G42) Quantizations, deformations for selfadjoint operator algebras (46L65) Quantum groups (operator algebraic aspects) (46L67)

Cites Work

• Equivariant Fredholm modules for the full quantum flag manifold of \(\mathrm{SU}_q(3)\)
• Comparison of unitary duals of Drinfeld doubles and complex semisimple Lie groups
• Equivariant Poincaré duality for quantum group actions
• Quantum deformation of Lorentz group
• On the regular representation of a nonunimodular locally compact group
• An algebraic framework for group duality
• Harmonic analysis on the quantum Lorentz group
• Unitary spherical representations of Drinfeld doubles
• On the Bernstein-Gelfand-Gelfand resolution for Kac-Moody algebras and quantized enveloping algebras
• Quantum Groups: Singular Vectors and BGG Resolution
• Amenability and Co-Amenability for Locally Compact Quantum Groups
• Verma module annihilators for quantized enveloping algebras
• The Plancherel Formula For Complex Semisimple Lie Groups
• Locally compact quantum groups
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