  A continuation of the joint work by Vadim Gorin and the author, J. Funct.
Anal. 270 (2016), 375-418; arXiv:1504.06832.
  The extended Gelfand-Tsetlin graph, introduced in that paper, is a novel
combinatorial object. Its q-boundary is formed by infinite point configurations
on a two-sided q-lattice. The q-boundary carries a continuous family of
probability measures that are a q-analogue of the so-called zw-measures, which
originated in the problem of harmonic analysis on the infinite-dimensional
unitary group.
  In the present paper, it is proved that certain transition Markov kernels,
linked to the extended Gelfand-Tsetlin graph and its q-boundary, possess the
Feller property. This property is needed for constructing a model of Markov
dynamics on the q-boundary. A connection with the classical B-splines and their
q-analogues is discussed. Some results of the paper arXiv:1504.06832 are
rederived in another way.
