Automorphic representations and harmonic cochains for GL_n+1

2010/05/14 by Yacine Aït Amrane, Amrane, Yacine Aït
Mathematics · #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT) #math.NT #math.RT

paper · pdf · doi:10.48550/arxiv.1005.2539

arxiv created 2010/05/14 · arxiv updated 2010/05/17

Abstract

Let K be a global field of positive characteristic. Let ∞ be a fixed place of K. This paper gives an explicit isomorphism between the space of automorphic forms (resp. cusp forms) for GL_n+1(K) that transform like the special representations and certain spaces of harmonic cochains (resp. those with finite support) defined on the Bruhat-Tits building of GL_n+1(K_∞).

Related

• Arithmetic quotients of the Bruhat-Tits building for projective general linear group in positive characteristic
• Rational Structures on Automorphic Representations
• Potential automorphy for certain Galois representations to GL₂n
• Multiplicities of cohomological automorphic forms on GL₂ and mod p representations of GL₂(ℚ_p)
• Level one algebraic cusp forms of classical groups of small ranks