Infinite tri-symmetric group, multiplication of double cosets, and checker topological field theories

Mathematics – Representation Theory

Scientific paper

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29 pages, 10 figures

Scientific paper

We consider a product of three copies of infinite symmetric group and its
representations spherical with respect to the diagonal subgroup. We show that
such representations generate functors from a certain category of simplicial
two-dimensional surfaces to the category of Hilbert spaces and bounded linear
operators.

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