A note on cusp forms and representations of SL₂(\mathbbF_p)

2018/11/01 by Zhe Chen, Chen, Zhe
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1811.00397

openalex publication_date 2018/11/01 · openalex created_date 2018/11/09 · openalex updated_date 2026/07/28

Abstract

Cusp forms are certain holomorphic functions defined on the upper half-plane, and the space of cusp forms for the principal congruence subgroup Γ(p), p a prime, is acted by SL₂(\mathbbF_p). Meanwhile, there is a finite field incarnation of the upper half-plane, the Deligne--Lusztig (or Drinfeld) curve, whose cohomology space is also acted by SL₂(\mathbbF_p). In this note we compute the relation between these two spaces in the weight 2 case.

Related

• Class numbers and invariant characters of \mathfraksl₂(\mathbbF_p)
• On Drinfeld cusp forms of prime level
• On the dimensions of certain spaces of vector-valued cusp forms
• Computing actions on cusp forms
• Dimension formulas for certain spaces of Drinfeld cusp forms