The Cauchy Harish-Chandra Integral, for the pair $$\mathfrak{u}_{p,q} ,\mathfrak{u}_1 $$

Andrzej Daszkiewicz, Tomasz Przebinda
2007 Central European Journal of Mathematics  
For the dual pair considered, the Cauchy Harish-Chandra Integral, as a distribution on the Lie algebra, is the limit of the holomorphic extension of the reciprocal of the determinant. We compute that limit explicitly in terms of the Harish-Chandra orbital integrals.
doi:10.2478/s11533-007-0023-3 fatcat:ufjlodxiibe5bfdlfnsga3vwny