On some conjectures of the unitary dual of U(p,q)

2022/10/17 by Kayue Daniel Wong, Wong, Kayue Daniel
Computer Science · Mathematics · #Coding theory and cryptography #Advanced Combinatorial Mathematics #Advanced Algebra and Geometry

paper · pdf · doi:10.48550/arxiv.2210.08684

Abstract

In this manuscript, we introduce the notion of fundamental cases to study the unitary dual of U(p,q). As applications, we prove of a conjecture of Salamanca-Riba and Vogan stated in 1998, as well as the fundamental parallelepiped (FPP) conjecture of Vogan in 2023 for U(p,q).

Related

• The unitary dual of U(n,2)
• Vogan’s FPP conjecture for complex Lie groups
• The FPP Conjecture for Real Reductive Groups
• On the non-vanishing of theta liftings of tempered representations of U(p,q)
• Unitaries Permuting Two Orthogonal Projections