The Bessel–Clifford Function Associated to the Cayley–Laplace Operator

Abstract

In this paper the Cayley–Laplace operator \(\Delta _{xu}\) is considered, a rotationally invariant differential operator which can be seen as a generalisation of the classical Laplace operator for functions depending on wedge variables \(X_{ab}\) (the minors of a matrix variable). We will show that the Bessel–Clifford function appears naturally in the framework of two-wedge variables, and explain how this function somehow plays the role of the exponential function in the framework of Grassmannians. This will be used to obtain a generalisation of the series expansion for the Newtonian potential, and to investigate a new kind of binomial polynomials related to Nayarana numbers.