On Generalized Weil Representations over Involutive Rings

2010/09/04 by Gutiérrez, Luis, J.C.F. Pantoja, Pantoja, José +2
Chemistry · Mathematics · #20C33 (Primary) #20H25 (Secondary) #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Carbohydrate Chemistry and Synthesis #FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1009.0877

openalex publication_date 2010/09/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct via generators and relations, generalized Weil representations for analogues of classical SL(2,k), k a field, over involutive base rings (A, ∗). This family of groups covers different kinds of groups, classical and non classical. We give some examples that include symplectic groups as well as non classical groups like SL_∗(2,A_m), where A_m is the finite modular analogue of the algebra of real m-jets in one dimension with its canonical involutive symmetry.

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