Regular Representation of the Quantum Heisenberg Double U_q(sl(2)), Fun_q(SL(2)) (q is a root of unity)

1993/11/12 by D. V. Gluschenkov, Gluschenkov, D. V., A. V. Lyakhovskaya +1
Mathematics · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Quantum Algebra (math.QA) #hep-th #math.QA

paper · pdf · doi:10.48550/arxiv.hep-th/9311075

UUITP-- 27/1993

arxiv created 1993/11/12 · arxiv updated 2009/11/30

Abstract

Pairing between the universal enveloping algebra U_q(sl(2)) and the algebra of functions over SL_q(2) is obtained in explicit terms. The regular representation of the quantum double is constructed and investigated. The structure of the root subspaces of the Casimir operator is revealed and described in terms of SL_q(2) elements.

Related

• Heisenberg double and Drinfeld double of the quantum superplane
• The Heisenberg double of the quantum Euclidean group and its representations
• Representation category of the quantum double of \rm SL(2,q)
• Quantum double construction in the C*-algebra setting of certain Heisenberg-type quantum groups
• Quantum Heisenberg Enveloping Algebra