Work

Cohomological representations for real reductive groups

Year: 2021

Type: article

Abstract: For a connected reductive group G over R, we study cohomological A-parameters, which are Arthur parameters with the infinitesimal character of a finite-dimensional representation of G ( C ) . We prove a structure theorem for such A-parameters, and deduce from it that a morphism of L-groups which takes a regular unipotent element to a regular unipotent element respects cohomological A-parameters. This is used to give complete understanding of cohomological A-parameters for all classical groups. We review the parametrization of Adams–Johnson packets of cohomological representations of G ( R ) by cohomological A-parameters and discuss various examples. We prove that the sum of the ranks of cohomology groups in a packet on any real group (and with any infinitesimal character) is independent of the packet under consideration, and can be explicitly calculated. This result has a particularly nice form when summed over all pure inner forms.

Source: Journal of the London Mathematical Society

DOI: 10.1112/jlms.12468

Authors: Arvind N. Nair, Dipendra Prasad

Institutions: Tata Institute of Fundamental Research, Indian Institute of Technology Bombay

Language: English

Topic: Advanced Algebra and Geometry

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Department of Atomic Energy, Government of India, Science and Engineering Research Board

Awards: G2243882444, G4753045903