Nonunitary Representations of the Groups of U(p, q)-currents for q ≥ p > 1
- Authors: Vershik A.M.1,2, Graev M.I.3
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Affiliations:
- St.Petersburg Department of Steklov Institute of Mathematics and St. Petersburg State University
- Institute for Information Transmission Problems
- Institute for System Analysis
- Issue: Vol 232, No 2 (2018)
- Pages: 99-120
- Section: Article
- URL: https://journal-vniispk.ru/1072-3374/article/view/241270
- DOI: https://doi.org/10.1007/s10958-018-3861-6
- ID: 241270
Cite item
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
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