Unitary representations attached to parabolic subgroups: the case of abelian unipotent radical

2025/10/13 by Dan Ciubotaru, Ciubotaru, Dan
Mathematics · #Graph theory and applications

paper · pdf · doi:10.48550/arxiv.2510.11862

Abstract

We classify the unitary representations with integral infinitesimal character in Lusztig's category of unipotent representations in the case when the geometric parameter space comes from the action of a Levi subgroup on the abelian nilradical of a (maximal) parabolic subalgebra. We organise the unitary representations into microlocal Arthur packets. This is a test case for investigating a conjectural description of unitary representations with integral infinitesimal character.

Citations

• The FPP Conjecture for p-adic Groups
• The FPP Conjecture for Real Reductive Groups
• On the generalized Ramanujan and Arthur conjectures over function fields
• Wavefront Sets of Unipotent Representations of Reductive p-adic Groups II
• Hermitian forms for affine Hecke algebras
• Multiplicity matrices for the affine graded Hecke algebra
• Unitary spherical spectrum for split classical groups
• Classification of unipotent representations of simple p-adic groups,II

Related

• Explicit Hilbert spaces for certain unipotent representations III
• Parabolically induced unitary representations of the universal group\n U(F)⁺ are C₀
• Integral models of unitary representations of current groups with values in semidirect products
• Towards a Goldberg-Shahidi pairing for classical groups
• The parabolic algebra revisited