The inverse of the Abel transform on ${\bf SU}^{\star}(2n)/{\bf Sp}(n)$

Abstract

In this note, we study the inverse of the Abel transform for the symmetric space SU⋆(2n)/Sp(n). We start by giving a recursive formula for the dual of the Abel transform on the root system An−1. This formula allows us to consider a transmutation property on the generalized Abel transform associated to An−1.