We develop a simple algebraic approach to the study of the Weil representation associated to a finite abelian group. As a result, we obtain a simple proof of a generalisation of a well-known formula for the absolute value of its character. We also obtain a new result about its decomposition into irreducible representations. As an example, the decomposition of the Weil representation of Sp2g(Z/N...

The Jacobi group is the semi-direct product of the symplectic group and the Heisenberg group. The Jacobi group is an important object in the framework of quantum mechanics, geometric quantization and optics. In this paper, we study the Weil representations of the Jacobi group and their properties. We also provide their applications to the theory of automorphic forms on the Jacobi group and repr...

We review definitions of generalized parallel transports in terms of Cheeger-Simons differential characters. Integration formulae are given in terms of Deligne-Beilinson cohomology classes. These representations of parallel transport can be extended to situations involving distributions as is appropriate in the context of quantized fields. LAPTH-750/99 SPhT-T04/080

We review definitions of generalized parallel transports in terms of Cheeger-Simons differential characters. Integration formulae are given in terms of Deligne-Beilinson cohomology classes. These representations of parallel transport can be extended to situations involving distributions as is appropriate in the context of quantized fields. LAPTH-1099/05 SPhT-T04/080

Abstract In their renowned paper (2011, Inventiones Mathematicae 184, 591–627), I. Vollaard and T. Wedhorn defined a stratification on the special fiber of unitary unramified PEL Rapoport–Zink space with signature $(1,n-1)$ . They constructed an isomorphism between closure stratum, called closed Bruhat–Tits Deligne–Lusztig variety which is not classical type. this paper, we describe $\ell $ -ad...