  The Gamma kernel is a projection kernel of the form
(A(x)B(y)-B(x)A(y))/(x-y), where A and B are certain functions on the
one-dimensional lattice expressed through Euler's Gamma function. The Gamma
kernel depends on two continuous parameters; its principal minors serve as the
correlation functions of a determinantal probability measure P defined on the
space of infinite point configurations on the lattice. As was shown earlier
(Borodin and Olshanski, Advances in Math. 194 (2005), 141-202;
arXiv:math-ph/0305043), P describes the asymptotics of certain ensembles of
random partitions in a limit regime.
  Theorem: The determinantal measure P is quasi-invariant with respect to
finitary permutations of the nodes of the lattice.
  This result is motivated by an application to a model of infinite particle
stochastic dynamics.
