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

Abstract

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.

29 pages, 10 figures

References in corpus (1)

• Cyclic Foam Topological Field Theories

Cited by in corpus (7)

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• A remark on representations of infinite symmetric groups
• Infinite symmetric group and bordisms of pseudomanifolds
• Infinite symmetric group and combinatorial descriptions of semigroups of double cosets
• Multiplication of conjugacy classes, colligations, and characteristic functions of matrix argument
• A Product on Double Cosets of $B_{\infty }$
• Several remarks on groups of automorphisms of free groups