On the group of infinite $p$-adic matrices with integer elements

Abstract

Let $G$ be an infinite-dimensional real classical group containing the complete unitary group (or complete orthogonal group) as a subgroup. Then $G$ generates a category of double cosets (train) and any unitary representation of $G$ can be canonically extended to the train. We prove a technical lemma about the complete group $GL$ of infinite $p$-adic matrices with integer coefficients, this lemma implies that the phenomenon of automatic extension of unitary representations to trains is valid for infinite-dimensional $p$-adic groups.

arXiv comment15p

References in corpus (2)

• Multi-operator colligations and multivariate characteristic functions
• Infinite symmetric group and bordisms of pseudomanifolds

Cited by in corpus (1)

• Groups $GL(\infty )$ over finite fields and multiplications of double cosets