Cohomological representations for real reductive groups

Autor: Nair, Arvind, Prasad, Dipendra
Rok vydání: 2019
Předmět:
Druh dokumentu: Working Paper
DOI: 10.1112/jlms.12468
Popis: For a connected reductive group $G$ over ${\mathbb R}$, we study cohomological $A$-parameters, which are Arthur parameters with the infinitesimal character of a finite-dimensional representation of $G({\mathbb C})$. 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 $G({\mathbb R})$ 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.
Comment: Considerably streamlined version. To appear in the Journal of the London Math Society
Databáze: arXiv