A bstract We derive manifestly covariant actions of spinning particles starting from coadjoint
orbits of isometry groups, by using Hamiltonian reductions. We show that the defining …

These notes are intended to provide an introduction to the theory of the theta
correspondence over a nonarchimdean local field. They form the basis and background for …

The recent proposal by Ben-Zvi, Sakellaridis and Venkatesh of a duality in the relative
Langlands program, leads, via the process of quantization of Hamiltonian varieties, to a …

We study the action of the derived Hecke algebra in the setting of dihedral weight one forms
and prove a conjecture of the second-and fourth-named authors relating this action to …

The main goal of this expository article is to survey recent progress on the arithmetic Siegel–
Weil formula and its applications. We begin with the classical sum of two squares problem …

We analyze holomorphic Jacobi forms of weight one with level. One such form plays an
important role in umbral moonshine, leading to simplifications of the statements of the …

These notes were written for the workshop on the Theta correspondence held at the
University of Maryland, May 1994. They have circulated informally for many years. Except for …

The spinor-helicity representations of massive and (partially) massless particles in four-
dimensional (anti–) de Sitter (A) dS spacetime are studied within the framework of the dual …

A bstract We study general aspects of the reductive dual pair correspondence, also known
as Howe duality. We make an explicit and systematic treatment, where we first derive the …

In this paper, we consider higher tensor powers of oscillator representations over finite
fields. We find a decomposition of their endomorphism algebras into group algebras of …