On explicit realization of algebra of complex powers of generators of U_q(\mathfraksl(3))

2020/10/29 by Sultanich, Pavel
#FOS: Mathematics #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.2010.15567

Abstract

In this note we prove an integral identity involving complex powers of generators of quantum group U_q(\mathfraksl(3)) considered as certain positive operators in the setting of positive principal series representations. This identity represents a continuous analog of one of the Lusztig's relations between divided powers of generators of quantum groups, which play an important role in the study of irreducible modules \citeLu 1. We also give definitions of arbitrary functions of U_q(\mathfraksl(3)) generators and give another proofs for some of the known results concerning positive principal series representations of U_q(\mathfraksl(3)).

Related

• On explicit realization of algebra of complex divided powers of U_q(\mathfraksl(2))
• Positive representations of split real quantum groups and future perspectives
• Positive representations of non-simply-laced split real quantum groups
• Complex semisimple quantum groups and representation theory
• The Lusztig automorphism of U_q( mathfraksl₂) from the equitable\n point of view