Classification of GL_n(ℂ)-Representations Distinguished by GL_n(ℝ)

2025/01/24 by Basudev Pattanayak, William Ka Kei Wu, Pattanayak, Basudev +3
Mathematics · Computer Science · #Advanced Algebra and Geometry #Finite Group Theory Research #Coding theory and cryptography

paper · pdf · doi:10.48550/arxiv.2501.14449

Abstract

This paper provides a complete classification of GL_n(ℝ)-distinguished irreducible representations of GL_n(ℂ) when the representations are either generic or unitary. Additionally, for each such GL_n(ℝ)-distinguished representation, we explicitly construct the associated period and prove its non-vanishing on the distinguished minimal K-type. Furthermore, we offer some applications to the branching problem using theta correspondence.

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