Weyl groups, the Dirac inequality, and isolated unitary unramified representations

2020/11/05 by Dan Ciubotaru, Ciubotaru, Dan · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models

paper · pdf · doi:10.48550/arxiv.2011.03100

Abstract

I present several applications of the Dirac inequality to the determination of isolated unitary representations and associated "spectral gaps" in the case of unramified principal series. The method works particularly well in order to attach irreducible unitary representations to the large nilpotent orbits (e.g., regular, subregular) in the Langlands dual complex Lie algebra. The results could be viewed as a p-adic analogue of Salamanca-Riba's classification of irreducible unitary (\mathfrak g,K)-modules with strongly regular infinitesimal character.

Cited by

• Some unipotent Arthur packets for p-adic split F4

Related

• Dirac inequality for highest weight Harish-Chandra modules I
• Dirac series for complex classical Lie groups: A multiplicity-one theorem
• On restriction of unitarizable representations of general linear groups and the non-generic local Gan-Gross-Prasad conjecture
• Dirac series of GL(n, ℝ)
• The wavefront set: bounds for the Langlands parameter