In this paper we consider two Rankin-Selberg integrals which were discovered by David Ginzburg, and announced in [G-H1]. These integrals are defined on a split form of GSO2n (see below for precise definition), and involve a generic cuspidal automorphic representation of this group. We content ourselves with showing that both integrals unfold to Eulerian integrals involving Whittaker functions, ...

Abstract We study the Picard–Lefschetz formula for Siegel modular threefolds of paramodular level and prove weight-monodromy conjecture its middle degree inner cohomology. give some applications to Langlands programme: using Rapoport-Zink uniformisation supersingular locus special fiber, we construct a geometric Jacquet–Langlands correspondence between $${\text {GSp}}_4$$ <mml:math xmlns:mml="h...

This paper gives a Langlands classification of constituents of ramified principal series representations for split p-adic groups with connected center.

Certain non-tempered liftings from PGL(2) × PGL(2) to PGSp(4) are constructed using the theory of (local and global) theta lifts. The resulting representations on PGSp(4) are the Saito–Kurokawa representations. The lifting is shown to be functorial under certain reasonable assumptions on the local Langlands correspondence for PGSp(4).

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In this paper we show that the Baues-Wirsching complex used to define cohomology of categories is a 2-functor from a certain 2-category of natural systems of abelian groups to the 2-category of chain complexes, chain homomorphism and relative homotopy classes of chain homotopies. As a consequence we derive (co)localization theorems for this cohomology.

We specify two problems in syllogistic: the lack of functoriality of predicates (although a thief is a person, a good thief may not be a good person) and the change of grammatical role of the middle term, from subject to predicate, in some syllogisms. The standard semantics, the class interpretation, by-passes these difficulties but, we argue, in a manner that is at odds with logical intuition....

This paper aims to contribute to the study of algebras with triangular decomposition over a Hopf algebra, as well as the BGG Category O. We study functorial properties of O across various setups. The first setup is over a skew group ring, involving a finite group Γ acting on a regular triangular algebra A. We develop Clifford theory for A⋊Γ, and obtain results on block decomposition, complete r...

Abstract We calculate, in the framework of geometric Langlands program, periods cuspidal automorphic sheaves for $\operatorname{GL}_{2n}$ along Levi subgroup $\operatorname{GL}_n\times \operatorname{GL}_n$. also solve corresponding local problem.

In the late 1960’s, Robert Langlands introduced a number of ideas to the theory of automorphic forms and formulated a number of conjectures which gave the theory a new focus. I was a colleague of his at this time, and a good deal of my professional energy since then has been directed to problems posed by him. Thus it was not entirely inappropriate that when I was invited to this conference, Miy...