Multiplication of conjugacy classes, colligations, and characteristic functions of matrix argument

Abstract

We extend the classical construction of operator colligations and characteristic functions. Consider the group $G$ of finite block unitary matrices of size $\alpha +\infty +...+\infty$ ($k$ times). Consider the subgroup $K=U(\infty )$, which consists of block diagonal unitary matrices (with a block 1 of size $\alpha$ and a matrix $u\in U(\infty )$ repeated $k$ times). It appears that there is a natural multiplication on the conjugacy classes $G//K$. We construct 'spectral data' of conjugacy classes, which visualize the multiplication and are sufficient for a reconstruction of a conjugacy class.

20pp, extended version

References in corpus (3)

• Multi-operator colligations and multivariate characteristic functions
• Infinite symmetric group and bordisms of pseudomanifolds
• On concentration of convolutions of double cosets at infinite-dimensional limit

Cited by in corpus (2)

• Algebras of conjugacy classes in symmetric groups
• Inner functions of matrix argument and conjugacy classes in unitary groups