Nilpotent Lie Groups in Clifford Analysis: Five Directions for Research

2000/09/10 by Vladimir V. Kisil
Physics and Astronomy · Mathematics · #math-ph #math.MP #msc:30G35 #msc:22E27 #msc:43A85 #msc:47A60 #msc:47G #msc:81R30 #msc:81S10

paper · pdf

published as F. Bracks et al. (eds.) Clifford Analysis and Its Applications, 135-141, 2001 Kluwer Academic Publishers · LaTeX2e, 7 pages

arxiv created 2000/09/10 · arxiv updated 2009/11/30

Abstract

The aim of the paper is to popularise nilpotent Lie groups (notably the Heisenberg group and alike) in the context of Clifford analysis and related models of mathematical physics. It is argued that these groups are underinvestigated in comparison with other classical branches of analysis. We list five general directions which seem to be promising for further research. Keywords: Clifford analysis, Heisenberg group, nilpotent Lie group, Segal-Bargmann space, Toeplitz operators, singular integral operators, pseudodifferential operators, functional calculus, joint spectrum, quantum mechanics, spinor field.

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