论文标题
二面dunkl-dirac操作员对称代数的有限维表示
Finite-dimensional representations of the symmetry algebra of the dihedral Dunkl--Dirac operator
论文作者
论文摘要
dunkl- dirac操作员是通过dunkl衍生物对狄拉克操作员的变形。我们研究了由dunkl--dirac操作员及其双重符号产生的对称代数。该对称代数在Clifford代数的张量产物内实现，以及与反射组或根系相关的有理Cherednik代数。对于第三等级的可简化根系，我们确定了所有不可约定的有限维表示和单位性的条件。 dunkl- dirac方程的多项式解决方案是作为一种这种不可还原统一表示的家族的实现。
The Dunkl--Dirac operator is a deformation of the Dirac operator by means of Dunkl derivatives. We investigate the symmetry algebra generated by the elements supercommuting with the Dunkl--Dirac operator and its dual symbol. This symmetry algebra is realised inside the tensor product of a Clifford algebra and a rational Cherednik algebra associated with a reflection group or root system. For reducible root systems of rank three, we determine all the irreducible finite-dimensional representations and conditions for unitarity. Polynomial solutions of the Dunkl--Dirac equation are given as a realisation of one family of such irreducible unitary representations.
