Endoscopic transfer and automorphic L-functions: the case of the general spin group and the twisted symmetric and exterior square L-functions

The endoscopic classification and the Langlands spectral theory are two approaches to the discrete spectrum of the group of adèlic points of a reductive linear algebraic group defined over a number field. The two points of view on the same object yield interesting consequences. In this paper, the case of the general spin group is considered. In that case, it is shown how the comparison of the two approaches implies that the twisted symmetric and exterior square complete automorphic L-functions associated to a cuspidal automorphic representation of the general linear group are holomorphic in the critical strip

The Tadić philosophy: An overview of the guiding principles and underlying ideas in the work of Marko Tadić

This paper provides an overview of the guiding principles and underlying ideas in the work of Marko Tadić. His research is mostly concerned with the representation theory of reductive groups over local fields. From the authors\u27 perspective, the most important guiding principles in his work are the essential simplicity of harmonic analysis, even in the non-commutative non-compact case, the Lefschetz principle saying that the representation theory over archimedean and non-archimedean fields should be studied in a unified way, and the principle of comparison of Jacquet modules. Besides these, the most prominent and fruitful ideas are the structural external approach to the unitary dual, the unitarizability along the lines, the use of topology of various duals to get information in harmonic analysis and arithmetic of the underlying group, and the interplay between unitarizability and Arthur packets. All these principles and ideas are the subject of this paper

Note on reducibility of parabolic induction for hermitian quaternionic groups over p-adic fields

In this paper we study the reducibility of certain class of parabolically induced representations of $p$-adic hermitian quaternionic groups. We use the Jacquet modules techniques and the theory of ($R$)-groups to extend the reducibility results of Tadić for split classical groups to the case of arbitrary hermitian quaternionic group

On the residual spectrum of Hermitian quaternionic inner form of SO_8

In this paper we decompose the residual spectrum supported in the minimal parabolic subgroup of an inner form of the split group SO8. The approach is the Langlands spectral theory. However, since the group is non-quasi-split, it is out of the scope of the Langlands-Shahidi method and the new technique for the normalization of standard intertwining operators is developed. The decomposition shows interesting parts of the residual spectrum not appearing in the case of quasi-split groups

The Franke filtration of the spaces of automorphic forms supported in a maximal proper parabolic subgroup

The Franke filtration is a finite filtration of certain spaces of automorphic forms on the adèlic points of a reductive linear algebraic group defined over a number field whose quotients can be described in terms of parabolically induced representations. Decomposing the space of automorphic forms according to their cuspidal support, the Franke filtration can be made more explicit. This paper describes explicitly the Franke filtration of the spaces of automorphic forms supported in a maximal proper parabolic subgroup, that is, in a cuspidal automorphic representation of its Levi factor. Such explicit description is important for applications to computation of automorphic cohomology, and thus the cohomology of congruence subgroups. As examples, the general linear group and split symplectic and special orthogonal groups are treated