A5021221955- Holomorphic and Operator Theory
- Advanced Topics in Algebra
- Algebraic and Geometric Analysis
- Algebraic structures and combinatorial models
- Nonlinear Waves and Solitons
- Spectral Theory in Mathematical Physics
- Mathematical Analysis and Transform Methods
- Advanced Algebra and Geometry
- Matrix Theory and Algorithms
Charles University
2008-2015
ZNA Middelheim Hospital
2010
University of Antwerp
2010
Recently, the Fischer decomposition for polynomials on superspace ℝm|2n (that is, in m commuting and 2n anti-commuting variables) has been obtained unless superdimension M = − is even non-positive. In this case, it turns out that of into spherical harmonics quite analogous as ℝm an irreducible under natural action Lie superalgebra 𝔬𝔰𝔭(m|2n). paper, we describe explicitly exceptional case when ∈ 2ℕ0. particular, show that, 𝔬𝔰𝔭(m|2n), not, general, a but just indecomposable pieces.
We study conformally invariant differential operators on functions valued in Spin(n)-representations with halfintegral highest weights (higher spin representations) the sphere. show that for most of these representations there is a unique such operator arbitrary odd order, and construct new examples weight (52,12,…12), using spectrum generating method by Branson, O/rsted Ólafsson [6]. These are higher analogs powers Dirac first constructed Liu Ryan [21].
We extend our previous results on spaces of polynomial invariants for Rarita‐Schwinger operators acting representations Sk with highest weight (k+12,12…,12) to a more general setting. This setting may be seen as toy model the study Higher Spin Dirac half‐integral weights, and already hints at an essential difference structure space invariant differential representation.
Recently, the Fischer decomposition for polynomials on superspace R^{m|2n} (that is, in m commuting and 2n anti-commuting variables) has been obtained unless superdimension M=m-2n is even non-positive. In this case, it turns out that of into spherical harmonics quite analogous as R^m an irreducible under natural action Lie superalgebra osp(m|2n). paper, we describe explicitly exceptional case when M particular, show that, osp(m|2n), not, general, a but indecomposable pieces.
This paper deals with the problem of factorizing integer powers Laplace operator acting on functions taking values in higher spin representations. is a far-reaching generalization well-known fact that square Dirac equal to operator. Using algebraic properties projections Stein-Weiss gradients, i.e. generalized Rarita-Schwinger and twistor operators, we give sharp upper bound order polyharmonicity for given representation half-integral highest weight.
Views Icon Article contents Figures & tables Video Audio Supplementary Data Peer Review Share Twitter Facebook Reddit LinkedIn Tools Reprints and Permissions Cite Search Site Citation Dalibor Šmíd; A fifth order conformally invariant higher spin operator on the sphere. AIP Conf. Proc. 26 September 2012; 1479 (1): 332–335. https://doi.org/10.1063/1.4756130 Download citation file: Ris (Zotero) Reference Manager EasyBib Bookends Mendeley Papers EndNote RefWorks BibTex toolbar search Dropdown...