Nonunitary representations of the groups of U(p,q)-currents for q≥ p>1

2017/12/12 by Анатолий Моисеевич Вершик, Vershik, A. M., М. И. Граев +1
Mathematics · #22E25 #22E66 #Advanced Algebra and Geometry #Advanced Operator Algebra Research #FOS: Mathematics #Finite Group Theory Research #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1712.04497

openalex publication_date 2017/12/12 · openalex created_date 2024/04/10 · openalex updated_date 2026/07/28

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. Key words: Iwasawa subgroup, cohomology, group of currents, nonunitary representations.

Related

• Cohomology in nonunitary representations of semisimple Lie groups (the group U(2,2))
• Cohomology of Iwasawa subgroup of the group U(p,p) in nonunitary\n representations
• Special representations of nilpotent Lie groups and the associated Poisson representations of current groups
• Integral models of unitary representations of current groups with values in semidirect products
• Irreducible unitary representations with non-zero relative Lie algebra cohomology of the Lie group SO₀(2,m)