Combinatorial aspects of the Baker–Akhiezer functions for S2

Abstract

We show here that a certain sequence of polynomials arising in the study of S 2 m -quasi invariants satisfies a 3-term recursion. This leads to the discovery that these polynomials are closely related to the Bessel polynomials studied by Luc Favreau. This connection reveals a variety of combinatorial properties of the sequence of Baker–Akhiezer functions for S 2. In particular we obtain in this manner their generating function and show that it is equivalent to several further identities satisfied by these functions.