Disjointness of representations arising in harmonic analysis on the infinite-dimensional unitary group

Understand

We prove pairwise disjointness of representations T_{z,w} of the infinite-dimensional unitary group.

• These representations provide a natural generalization of the regular representation for the case of "big" group U(\infty).
• They were introduced and studied by G.Olshanski and A.Borodin.
• Disjointness of the representations can be reduced to disjointness of certain probability measures on the space of paths in the Gelfand-Tsetlin graph.