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

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.

Authors:
 [1]
  1. Institute for System Analysis (Russian Federation)
Publication Date:
OSTI Identifier:
22774013
Resource Type:
Journal Article
Journal Name:
Journal of Mathematical Sciences
Additional Journal Information:
Journal Volume: 232; Journal Issue: 2; Other Information: Copyright (c) 2018 Springer Science+Business Media, LLC, part of Springer Nature; http://www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1072-3374
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; CURRENTS; HILBERT SPACE; IRREDUCIBLE REPRESENTATIONS; NONUNITARY REPRESENTATIONS; U GROUPS

Citation Formats

Vershik, A. M., E-mail: avershik@gmail.com, and Graev, M. I. Nonunitary Representations of the Groups of U(p, q)-currents for q ≥ p > 1. United States: N. p., 2018. Web. doi:10.1007/S10958-018-3861-6.
Vershik, A. M., E-mail: avershik@gmail.com, & Graev, M. I. Nonunitary Representations of the Groups of U(p, q)-currents for q ≥ p > 1. United States. doi:10.1007/S10958-018-3861-6.
Vershik, A. M., E-mail: avershik@gmail.com, and Graev, M. I. Sun . "Nonunitary Representations of the Groups of U(p, q)-currents for q ≥ p > 1". United States. doi:10.1007/S10958-018-3861-6.
@article{osti_22774013,
title = {Nonunitary Representations of the Groups of U(p, q)-currents for q ≥ p > 1},
author = {Vershik, A. M., E-mail: avershik@gmail.com and Graev, M. I.},
abstractNote = {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.},
doi = {10.1007/S10958-018-3861-6},
journal = {Journal of Mathematical Sciences},
issn = {1072-3374},
number = 2,
volume = 232,
place = {United States},
year = {2018},
month = {7}
}