Nonunitary Representations of the Groups of U(p, q)-currents for q ≥ p > 1


Cite item

Full Text

Open Access Open Access
Restricted Access Access granted
Restricted Access Subscription Access

Abstract

The purpose of this paper is to give a construction of representations of the group of currents for semisimple groups of rank greater than one. Such groups have no unitary representations in the Fock space, since the semisimple groups of this form have no nontrivial cohomology in faithful irreducible representations. Thus we first construct cohomology of the semisimple groups in nonunitary representations. The principal method is to reduce all constructions to Iwasawa subgroups (solvable subgroups of the semisimple groups), with subsequent extension to the original group. The resulting representation is realized in the so-called quasi-Poisson Hilbert space associated with natural measures on infinite-dimensional spaces.

About the authors

A. M. Vershik

St.Petersburg Department of Steklov Institute of Mathematics and St. Petersburg State University; Institute for Information Transmission Problems

Author for correspondence.
Email: avershik@gmail.com
Russian Federation, St. Petersburg; Moscow

M. I. Graev

Institute for System Analysis

Email: avershik@gmail.com
Russian Federation, Moscow

Supplementary files

Supplementary Files
Action
1. JATS XML

Copyright (c) 2018 Springer Science+Business Media, LLC, part of Springer Nature