Structure of the kernel of higher spin Dirac operators

Martin Plechšmíd

Commentationes Mathematicae Universitatis Carolinae (2001)

  • Volume: 42, Issue: 4, page 665-680
  • ISSN: 0010-2628

Abstract

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Polynomials on ℝ n with values in an irreducible Spin n -module form a natural representation space for the group Spin n . These representations are completely reducible. In the paper, we give a complete description of their decompositions into irreducible components for polynomials with values in a certain range of irreducible modules. The results are used to describe the structure of kernels of conformally invariant elliptic first order systems acting on maps on ℝ n with values in these modules.

How to cite

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Plechšmíd, Martin. "Structure of the kernel of higher spin Dirac operators." Commentationes Mathematicae Universitatis Carolinae 42.4 (2001): 665-680. <http://eudml.org/doc/248778>.

@article{Plechšmíd2001,
abstract = {Polynomials on $\mathbb \{R\}^n$ with values in an irreducible $\operatorname\{Spin\}_n$-module form a natural representation space for the group $\operatorname\{Spin\}_n$. These representations are completely reducible. In the paper, we give a complete description of their decompositions into irreducible components for polynomials with values in a certain range of irreducible modules. The results are used to describe the structure of kernels of conformally invariant elliptic first order systems acting on maps on $\mathbb \{R\}^n$ with values in these modules.},
author = {Plechšmíd, Martin},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {conformally invariant differential operators; generalized (higher-spin) Dirac operators; representations of spin-groups; Littlewood-Richardson rule; conformally invariant differential operators; higher-spin Dirac operator; Littlewood-Richardson rule},
language = {eng},
number = {4},
pages = {665-680},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Structure of the kernel of higher spin Dirac operators},
url = {http://eudml.org/doc/248778},
volume = {42},
year = {2001},
}

TY - JOUR
AU - Plechšmíd, Martin
TI - Structure of the kernel of higher spin Dirac operators
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2001
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 42
IS - 4
SP - 665
EP - 680
AB - Polynomials on $\mathbb {R}^n$ with values in an irreducible $\operatorname{Spin}_n$-module form a natural representation space for the group $\operatorname{Spin}_n$. These representations are completely reducible. In the paper, we give a complete description of their decompositions into irreducible components for polynomials with values in a certain range of irreducible modules. The results are used to describe the structure of kernels of conformally invariant elliptic first order systems acting on maps on $\mathbb {R}^n$ with values in these modules.
LA - eng
KW - conformally invariant differential operators; generalized (higher-spin) Dirac operators; representations of spin-groups; Littlewood-Richardson rule; conformally invariant differential operators; higher-spin Dirac operator; Littlewood-Richardson rule
UR - http://eudml.org/doc/248778
ER -

References

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