This thesis is concerned with the structure theory of generalized Levi subgroups G of simply-connected Chevalley groups defined over a finite extension of a p-adic field. We present a geometric parameterization of this structure known as the Bruhat-Tits building B(G). The building facilitates visualizing and reasoning about the structure ofG, and therefore has applications to all things related...

For moduli space of stable parabolic bundles on a compact Riemann surface, we derive an explicit formula for the curvature of its canonical line bundle with respect to Quillen’s metric and interprete it as a local index theorem for the family of ∂̄-operators in the associated parabolic endomorphism bundles. The formula consists of two terms: one standard (proportional to the canonical Kähler for...

In analogy with the study of representations of GL2n(F ) distinguished by Sp 2n(F ), where F is a local field, in this paper we study representations of U2n(F ) distinguished by Sp2n(F ). (Only quasi-split unitary groups are considered in this paper since they are the only ones which contain Sp 2n(F ).) We prove that there are no cuspidal representations of U2n(F ) distinguished by Sp2n(F ) for...

The workspace topologies of a family of 3-revolute (3R) positioning manipulators are enumerated. The workspace is characterized in a half-cross section by the singular curves. The workspace topology is defined by the number of cusps that appear on these singular curves. The design parameters space is shown to be divided into five domains where all manipulators have the same number of cusps. Eac...

In their paper which introduced Monsky-Washnitzer cohomology, Monsky and Washnitzer described conditions under which the definition can be adapted to give integral cohomology groups. It seems to be well-known among experts that their construction always gives well-defined integral cohomology groups, but this fact also does not appear to be explicitly written down anywhere. In this paper, we pro...

In this chapter we give a categorical definition of the integral cohomology ring of a stack. For quotient stacks [X/G] the categorical cohomology ring may be identified with the equivariant cohomology H∗ G(X). Identifying the stack cohomology ring with equivariant cohomology allows us to prove that the cohomology ring of a quotient Deligne-Mumford stack is rationally isomorphic to the cohomolog...

Hecke operators play an important role in the theory of automorphic forms, and automorphic forms are closely linked to various cohomology groups. This paper is mostly a survey of Hecke operators acting on certain types of cohomology groups. The class of cohomology on which Hecke operators are introduced includes the group cohomology of discrete subgroups of a semisimple Lie group, the de Rham c...

Let F be a number field and K a quadratic algebra over F , i.e., either F × F or a quadratic field extension of F . Denote by G the F -group defined by GL(2)/K. Then, given any cuspidal automorphic representation π of G(AF ), one has (cf. [8], [9]) a transfer to an isobaric automorphic representation Π of GL4(AF ) corresponding to the L-homomorphism LG → LGL(4). Usually, Π is called the Rankin-...