207 citations · 2k across the 52 of their papers we have counts for
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The Gelfand-Tsetlin bases for Hodge-de Rham systems in Euclidean spaces
Richard Delanghe, Roman Lavicka, Vladimir Soucek
The main aim of this paper is to construct explicitly orthogonal bases for the spaces of k-homogeneous polynomial solutions of the Hodge-de Rham system in the Euclidean space R^m w…
The Fischer decomposition for Hodge-de Rham systems in Euclidean spaces
Richard Delanghe, Roman Lavicka, Vladimir Soucek
The classical Fischer decomposition of spinor-valued polynomials is a key result on solutions of the Dirac equation in the Euclidean space R^m. As is well-known, it can be understo…
The Gelfand-Tsetlin bases for spherical monogenics in dimension 3
S. Bock, K. Guerlebeck, R. Lavicka +1
The main aim of this paper is to recall the notion of the Gelfand-Tsetlin bases (GT bases for short) and to use it for an explicit construction of orthogonal bases for the spaces o…
Orthogonal basis for spherical monogenics by step two branching
R. Lavicka, V. Soucek, P. Van Lancker
Spherical monogenics can be regarded as a basic tool for the study of harmonic analysis of the Dirac operator in Euclidean space R^m. They play a similar role as spherical harmonic…
Canonical bases for sl(2,C)-modules of spherical monogenics in dimension 3
Roman Lavicka
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 bas…
The Fischer Decomposition for the H-action and Its Applications
Roman Lavicka
Recently the Fischer decomposition for the H-action of the Pin group on Clifford algebra valued polynomials has been obtained. We apply this tool to get various decompositions of s…