Gel’fand-Tsetlin procedure for the construction of orthogonal bases in Hermitean Clifford analysis

q-Deformed Orthogonal and Pseudo-Orthogonal Algebras and Their Representations

Deformed orthogonal and pseudo-orthogonal Lie algebras are constructed which differ from deformations of Lie algebras in terms of Cartan subalgebras and root vectors and which make it possible to construct representations by operators acting according to Gel’fand–Tsetlin-type formulas. Unitary representations of the q-deformed algebras Uq(son,1) are found. AMS subject classifications (1980). 16...

Orthogonal bases of Hermitean monogenic polynomials: an explicit construction in complex dimension 2

In this contribution we construct an orthogonal basis of Hermitean monogenic polynomials for the specific case of two complex variables. The approach combines group representation theory, see [5], with a Fischer decomposition for the kernels of each of the considered Dirac operators, see [4], and a Cauchy-Kovalevskaya extension principle, see [3].

Construction of Compactly Supported Nonseparable Orthogonal Wavelets of L^2(R^n)

Weight bases of Gelfand–Tsetlin type for representations of classical Lie algebras

This paper completes a series devoted to explicit constructions of finitedimensional irreducible representations of the classical Lie algebras. Here the case of odd orthogonal Lie algebras (of type B) is considered (two previous papers dealt with C and D types). A weight basis for each representation of the Lie algebra o(2n + 1) is constructed. The basis vectors are parametrized by Gelfand–Tset...

Fischer Decompositions in Euclidean and Hermitean Clifford Analysis

Euclidean Clifford analysis is a higher dimensional function theory studying so–called monogenic functions, i.e. null solutions of the rotation invariant, vector valued, first order Dirac operator ∂. In the more recent branch Hermitean Clifford analysis, this rotational invariance has been broken by introducing a complex structure J on Euclidean space and a corresponding second Dirac operator ∂...