2004/10/31 by Vladimir V. Kisil, Debapriya Biswas
Mathematics · #math.CV #math.GR #math.MG #msc:30G35 #msc:22E46
published as Trans. Inst. Math. of the NAS of Ukraine, v. 1(2004), no.3, pp.100--118 · 14 pages, AMS-LaTeX, 31 PS graphcs in 7 Figures; v2--the missing PS file is included now; v3 minor corrections, reference added; v4 numerous misprints corrected
arxiv created 2005/09/08 · arxiv updated 2009/12/01
This paper lays down a foundation for a systematic treatment of three main (elliptic, parabolic and hyperbolic) types of analytic function theory based on the representation theory of SL(2,R) group. We describe here geometries of corresponding domains. The principal role is played by Clifford algebras of matching types. Keywords: analytic function theory, semisimple groups, elliptic, parabolic, hyperbolic, Clifford algebras