2002/10/31 by Byung-Jay Kahng, Kahng, Byung-Jay
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Operator Algebras (math.OA) #Quantum Algebra (math.QA) #math.OA #math.QA
paper · pdf · doi:10.48550/arxiv.math/0211003
25 pages, 1 figure
openalex publication_date 2002/10/31 · arxiv created 2004/05/05 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, as a generalization of Kirillov's orbit theory, we explore the relationship between the dressing orbits and irreducible *-representations of the Hopf C*-algebras (A,Δ) and (A, Δ) we constructed earlier. We discuss the one-to-one correspondence between them, including their topological aspects. On each dressing orbit (which are symplectic leaves of the underlying Poisson structure), one can define a Moyal-type deformed product at the function level. The deformation is more or less modeled by the irreducible representation corresponding to the orbit. We point out that the problem of finding a direct integral decomposition of the regular representation into irreducibles (Plancherel theorem) has an interesting interpretation in terms of these deformed products.