We consider a generalization of the classical Laplace operator, which includes the Laplace–
Dunkl operator defined in terms of the differential-difference operators associated with finite …

The Darboux transformation (DT) for the super-integrable hierarchy has an essential
difference from the general system. As we know, the super-integrable soliton equation …

The decomposition of polynomials of one vector variable into irreducible modules for the
orthogonal group is a crucial result in harmonic analysis which makes use of the Howe …

Mathematics does not happen in a vacuum. Mathematicians, those who do mathematics, are
the people infusing life in the theory. Subjects are studied and established from sparks and …

We introduce a family of commuting generalised symmetries of the Dunkl–Dirac operator
inspired by the Maxwell construction in harmonic analysis. As an application, we use these …

The Lie algebra generated by $ m\$$ p $-dimensional Grassmannian Dirac operators and $
m\$$ p $-dimensional vector variables is identified as the orthogonal Lie algebra $\mathfrak …

Recently, the Fischer decomposition for polynomials on superspace ℝ m| 2n (that is,
polynomials in m commuting and 2n anti-commuting variables) has been obtained unless …

The aim of this paper is to obtain a generalized CK-extension theorem in superspace for the
biaxial Dirac operator ∂ _ x+ ∂ _ y∂ x+∂ y. In the classical commuting case, this result can …

The CCR (canonical commuting relation) and CAR algebras (canonical anticommuting
relation) are fundamental algebras in theoretical physics used for the study of bosons and …

There are two well-known ways of describing elements of the rotation group SO $(m) $. First,
according to the Cartan-Dieudonn\'e theorem, every rotation matrix can be written as an …