Canonical bases for sl(2,C)-modules of spherical monogenics in dimension 3

Abstract

Spaces of homogeneous spherical monogenics in dimension 3 can be considered naturally as sl(2,C)-modules. As finite-dimensional irreducible sl(2,C)-modules, they have canonical bases which are, by construction, orthogonal. In this note, we show that these orthogonal bases form the Appell system and coincide with those constructed recently by S. Bock and K. Guerlebeck. Moreover, we obtain simple expressions of elements of these bases in terms of the Legendre polynomials.

a revised version (some references added, Introduction changed ); accepted for publication in Proceedings of the Winter School, Srni, Czech Republic, 2010

References in corpus (4)

• The Gelfand-Tsetlin bases for spherical monogenics in dimension 3
• On the development of Bohr's phenomenon in the context of Quaternionic analysis and related problems
• The Gelfand-Tsetlin bases for Hodge-de Rham systems in Euclidean spaces
• Real-Part Estimates for Solutions of the Riesz System in ${\mathbb{R}}^3$

Cited by in corpus (5)

• The Gelfand-Tsetlin bases for spherical monogenics in dimension 3
• The Gelfand-Tsetlin bases for Hodge-de Rham systems in Euclidean spaces
• The Fischer decomposition for Hodge-de Rham systems in Euclidean spaces
• Orthogonal basis for spherical monogenics by step two branching
• On a three dimensional analogue to the holomorphic z-powers