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Group representations

Representation theory

A general approach to proving the irreducibility of representations of infinite-dimensional groups within the frame of Ismagilov's conjecture.

The generalized characteristic polynomial, corresponding resolvent and their application

Arxiv (2025)

A. V. Kosyak

We introduced previously the generalized characteristic polynomial defined by PC(λ)=detC(λ), where C(λ)=C+diag(λ1,…,λn) for C∈Mat(n,ℂ) and λ=(λk)nk=1∈ℂn and gave the explicit formula for PC(λ). In this article we define an analogue of the resolvent C(λ)−1, calculate it and the expression (C(λ)−1a,a) for a∈ℂn explicitly. The obtained formulas and their variants were applied to the proof of the irreducibility of unitary representations of some infinite-dimensional groups.

Arxiv (2025)

A. V. Kosyak