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

By Roman Lavicka. 2010

51 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/b099c5ae4a4e9189e6cb00df658a8572d578fa93

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In Algebra and Number Theory

1. V. Souček
2. Roman Lavicka

In Applied Mathematics

1. Roman Lavicka
2. V. Souček
3. K. Guerlebeck
4. S. Bock

Citations in the corpus

• The Gelfand-Tsetlin bases for spherical monogenics in dimension 3 (2010, background): “In [31], the GT bases for this case are obtained in quite a different way.”
• Complete Orthogonal Appell Systems for Spherical Monogenics (2011, background): “In [21], these bases in dimension 3 are constructed in another way.”