Multiplicity of Eisenstein series in cohomology and applications to GSp₄ and G₂

2020/10/06 by Mundy, Sam
#FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2010.02712

Abstract

We set up a general framework to compute the exact multiplicity with which certain automorphic representations appear in both the cuspidal and Eisenstein cohomology of locally symmetric spaces. We apply this machinery to Eisenstein series on GSp₄ and split G₂. In the case of G₂, we will also obtain new information about the archimedean components of certain CAP representations using Arthur's conjectures.

Related

• Arthur's multiplicity formula for GSp₄ and restriction to Sp₄
• Eisenstein cohomology classes for GL_N over imaginary quadratic fields
• Multiplicity one for certain paramodular forms of genus two
• Some Combinatorics in the Cancellation of Poles of Eisenstein Series for GL(n,\mathbbA_ℚ)
• A conjectural refinement of strong multiplicity one for GL(n)