Higher Spin Dirac Operators Between Spaces of Simplicial Monogenics in Two Vector Variables

Brackx, Fred; Eelbode, David; Voorde, Liesbet Van de

doi:10.1007/s11040-010-9085-8

Cited by 16 publications

(31 citation statements)

References 16 publications

(26 reference statements)

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“…For the ungraded case, see e.g. [3,9,14,16,22]. In the unified construction of Spin(m)-invariant generalized Cauchy-Riemann operators of Stein and Weiss (see [22]), the tensor product of the fundamental representation of so(m) with other so(m)-representations needs to be calculated.…”

Section: Introductionmentioning

confidence: 99%

On a class of tensor product representations for the orthosymplectic superalgebra

Coulembier

2013

Journal of Pure and Applied Algebra

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The spinor representations for osp(m|2n) are introduced. These generalize the spinors for so(m) and the symplectic spinors for sp(2n) and correspond to representations of the supergroup with supergroup pair (Spin(m) × M p(2n), osp(m|2n)). These spinor spaces are proved to be uniquely characterized as the completely pointed osp(m|2n)-modules. The main aim is to study the tensor product of these representations with irreducible finite dimensional osp(m|2n)-modules. Therefore a criterion for complete reducibility of tensor product representations of semisimple Lie superalgebras is derived. Finally the decomposition into irreducible osp(m|2n)-representations of the tensor product of the super spinor space with an extensive class of such representations is calculated and also cases where the tensor product is not completely reducible are studied.MSC 2010 : 17B10

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Section: Introductionmentioning

confidence: 99%

On a class of tensor product representations for the orthosymplectic superalgebra

Coulembier

2013

Journal of Pure and Applied Algebra

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“…In a series of recent papers, see e.g. [11,3,4], further generalizations of these higher spin Dirac operators (HSD operators) were studied in an attempt to describe properties of HSD operators within an encompassing framework. Doing so, we have been able to isolate a few related problems which need to be solved first in order to formulate an adequate theory.…”

Section: Introductionmentioning

confidence: 99%

Triple Monogenic Functions and Higher Spin Dirac Operators

et al. 2011

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In the Clifford analysis context a specific type of solutions for the higher spin Dirac operators Q k,l (k ≥ l ∈ N) is studied; these higher spin Dirac operators can be seen as generalizations of the classical Rarita-Schwinger operator. To that end subspaces of the space of triple monogenic polynomials are introduced and their algebraic structure is investigated. Also a dimensional analysis is carried out.

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“…[8,22]) , the study of higher spin (Stein-Weiss) and RaritaSchwinger operators (see e.g. [3,4,5,6,7,13,30]). The paper is organized as follows.…”

Section: Introductionmentioning

confidence: 99%

The Monogenic Fischer Decomposition: Two Vector Variables

Lancker

2011

Complex Anal. Oper. Theory

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In this paper we will present two proofs of the monogenic Fischer decomposition in two vector variables. The first one is based on the so-called "Harmonic Separation of Variables Theorem" while the second one relies on some simple dimension arguments. We also show that these decomposition are still valid under milder assumptions than the usual stable range condition. In the process, we derive explicit formula for the summands in the monogenic Fischer decomposition of harmonics.

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Higher Spin Dirac Operators Between Spaces of Simplicial Monogenics in Two Vector Variables

Abstract: The higher spin Dirac operator Q k,l acting on functions taking values in an irreducible representation space for so(m) with highest weight

Cited by 16 publications

References 16 publications

On a class of tensor product representations for the orthosymplectic superalgebra

On a class of tensor product representations for the orthosymplectic superalgebra

Triple Monogenic Functions and Higher Spin Dirac Operators

The Monogenic Fischer Decomposition: Two Vector Variables

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