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

Sawyer, Patrice2007-09-052007-09-052007-09-05https://laurentian.scholaris.ca/handle/10219/38This paper has not been published. However, it has been cited in peer reviewed venues.In this note, we study the inverse of the Abel transform for the symmetric space ${\bf SU}^{\star}(2n)/{\bf Sp}(n)$. We start by giving a recursive formula for the dual of the Abel transform on the root system $A_{n-1}$. This formula allows us to consider a transmutation property on the generalized Abel transform associated to $A_{n-1}$.enAbel transformsymmetric spaceroot systemThe inverse of the Abel transform on ${\bf SU}^{\star}(2n)/{\bf Sp}(n)$Article