The representation ring of the unitary groups and Markov processes of algebraic origin

The second part deals with a family of Markov processes on the dual object to the infinite-dimensional unitary group U(∞). These processes were defined in a joint work with Alexei Borodin (2012) [5]. The main result of the present paper consists in the derivation of an explicit expression for their infinitesimal generators. It is shown that the generators are implemented by certain second order partial differential operators with countably many variables, initially defined as operators on R.