2025/12/19 by Suvrajit Bhattacharjee, Bhattacharjee, Suvrajit, Olof Giselsson +3
Mathematics · #Algebraic structures and combinatorial models #Advanced Operator Algebra Research #Advanced Combinatorial Mathematics
paper · doi:10.48550/arxiv.2512.17690
Given a semisimple compact Lie group G and a nonzero dominant integral weight λ, the highest weight Gq-modules Vnλ form a subproduct system of finite dimensional Hilbert spaces. Using a conjectural asymptotic behavior of Clebsch-Gordan coefficients we identify the corresponding Cuntz-Pimsner algebras with algebras of quantized functions on homogeneous spaces of G. We also show that the gauge-invariant part of the Toeplitz algebra provides a model for convergence of full matrix algebras to quantum flag manifolds, complementing and generalizing results of Landsman and Rieffel for q=1 and results of Vaes-Vergnioux in the rank one case for q≠1. We verify our conjecture on Clebsch-Gordan coefficients for G=SU(n) and all weights that are either regular or multiples of the fundamental weight ω1. For λ=ω1, we also provide a detailed description of the Toeplitz and Cuntz-Pimsner algebras, generalizing results of Arveson on symmetric subproduct systems.