2024/01/24 by Ron Erez, Erez, Ron
Chemistry · Mathematics · #Advanced Algebra and Geometry #Axial and Atropisomeric Chirality Synthesis #FOS: Mathematics #Molecular spectroscopy and chirality #Number Theory (math.NT) #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2401.13469
openalex publication_date 2024/01/24 · openalex created_date 2024/01/26 · openalex updated_date 2026/07/28
This work is largely inspired by the 2003 Ph.D. thesis \citesnitz of Kobi Snitz. In his thesis, Snitz constructed two irreducible, automorphic, cuspidal representations π and π' of the metaplectic group G ( \mathbb A ) = \widetilde SL 2 ( \mathbb A ) where each representation is obtained from a different global theta lifts of certain non-trivial automorphic characters ξ and ξ' of the orthogonal groups H \mathbb A = O ( q, V ) ( \mathbb A ) and H \mathbb A '= O ( q', V' ) ( \mathbb A ) , respectively, where \mathbb A = \mathbb A \mathbb F is the adele ring of a number field \mathbb F . Snitz shows that for certain matching data of quadratic spaces and automorphic quadratic characters, that these two representations of G ( \mathbb A ) are isomorphic, i.e. π≅π'. The goal of this work is to reformulate and generalize Snitz's work to higher rank groups. Namely we wish to determine for which admissible data ( ( q, V ) ,ξ, ( q', V' ),ξ' ) satisfying certain local necessary conditions could an isomorphism possibly exist between two global theta lifts π and π' with respect to two reductive dual pairs H \mathbb A × G \mathbb A and H' \mathbb A × G \mathbb A and two non-trivial automorphic quadratic characters ξ and ξ' of the orthogonal groups H \mathbb A = O ( q, V ) ( \mathbb A ) and H \mathbb A '= O ( q', V' ) ( \mathbb A ) , respectively and the group G which is the symplectic or the metaplectic group.