1997/03/03 by S. Sinel’shchikov, S. Sinel'shchikov, Sinel'shchikov, S. +2
Mathematics · #81R50 (Primary) 81Q99 (Secondary) #Advanced Topics in Algebra #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA) #math.QA #msc:81Q99 #msc:81R50 #q-alg
paper · pdf · doi:10.48550/arxiv.q-alg/9703005
LaTeX 2.09, 23 pages, [email protected], [email protected], some misprints are corrected
openalex publication_date 1997/03/03 · arxiv created 1998/09/18 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A very well known result by Harish-Chandra claims that any Hermitian symmetric space of non-compact type admits a canonical embedding into a complex vector space V. The image of this embedding is a bounded symmetric domain in V. This work provides a construction of q-analogues of a polynomial algebra on V and the differential algebra of exterior forms on V. A way of producing a q-analogue of the bounded function algebra in a bounded symmetric domain is described. All the constructions are illustrated by detailed calculations in the case of the simplest Hermitian symmetric space SU(1,1)/U(1). The development of these ideas can be found in math.QA/9803110 and math.QA/9809038 .