Disjointness of representations arising in harmonic analysis on the infinite-dimensional unitary group - Mathematics > Representation TheoryReport as inadecuate




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Abstract: We prove pairwise disjointness of representations T {z,w} of theinfinite-dimensional unitary group. These representations provide a naturalgeneralization of the regular representation for the case of -big- groupU\infty. They were introduced and studied by G.Olshanski and A.Borodin.Disjointness of the representations can be reduced to disjointness of certainprobability measures on the space of paths in the Gelfand-Tsetlin graph. Weprove the latter disjointness using probabilistic and combinatorial methods.



Author: Vadim Gorin

Source: https://arxiv.org/



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