Poincare series and miraculous duality

2022/11/10 by Lin, Kevin
#Algebraic Geometry (math.AG) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2211.05282

Abstract

In the setting of global geometric Langlands, we show that miraculous duality on the stack of principal bundles on a curve intertwines the functor of Poincare series with the dual functor to Whittaker coefficients. We construct, for arbitrary parabolic subgroups, Jacquet functors controlling constant terms of Poincare series and Whittaker coefficients of Eisenstein series in local terms.

Related

• Geometric Eisenstein series
• Geometric Whittaker models and Eisenstein series for Mp₂
• Proof of the geometric Langlands conjecture III: compatibility with parabolic induction
• Parabolic geometric Eisenstein series and constant term functors
• The Langlands lemma and the Betti numbers of stacks of G--bundles on a curve