Englis, Miroslav et Xu, Hao, Higher Laplace-Beltrami Operators on Bounded Symmetric Domains, Acta mathematica Sinica. English series (Print) , 34(8), 2018, pp. 1297-1312
It was conjectured by the first author and Peetre that the higher Laplace.Beltrami operators generate the whole ring of invariant operators on bounded symmetric domains. We give a proof of the conjecture for domains of rank . 6 by using a graph manipulation of Kähler curvature tensor. We also compute higher order terms in the asymptotic expansions of the Bergman kernels and the Berezin transform on bounded symmetric domain.