Title: On the general linear group over arithmetic orders, related automorphic representations and corresponding cohomology groups
Speaker: Joachim Schwermer (University of Vienna)
Abstract: Orders in finite-dimensional algebras over number fields give rise to interesting locally symmetric spaces and algebraic varieties. Hilbert modular varieties or arithmetically defined hyperbolic 3-manifolds, compact ones as well as non-compact ones, are familiar examples. In this talk we discuss various cases related to the general linear group GL(2) over orders in division algebras of degree d defined over some number field. The underlying algebraic group is an inner form of the k-split group GL(2d). Geometry, arithmetic, and the theory of automorphic forms are interwoven in a most fruitful way in this work. We indicate a construction of automorphic representations that represent non-vanishing square-integrable cohomology classes for such arithmetically defined groups.
Seminar URL: https://research.math.osu.edu/numbertheory/
