Related papers: The basis problem for modular forms for the Weil r…

We study the well-posedness of the initial value (Cauchy) problem of vacuum Einstein-aether theory. The latter is a Lorentz-violating gravitational theory consisting of General Relativity with a dynamical timelike 'aether' vector field,…

By a global approach, we prove the arithmetic fundamental lemma conjecture for unitary groups in $n$ variables over $\mathbb{Q}_p$ when $p\geq n$.

Siegel defined zeta functions associated with indefinite quadratic forms, and proved their analytic properties such as analytic continuations and functional equations. Coefficients of these zeta functions are called measures of…

We consider newform vectors in cuspidal representations of $p$-adic general linear groups. We extend the theory from the complex setting to include~$\ell$-modular representations with~$\ell\neq p$, and prove that the conductor is compatible…

In a previous work the authors gave a conceptual explanation for the linearity of the Weil representation over a finite field k of odd characteristic: There exists a canonical system of intertwining operators between the Lagrangian models…

Let F be the usual real field. Let W be a symplectic vector space over F. It is known that there are two different Weil representations of a Meteplectic covering group $\widetilde{Sp}(W)$. By some twisted actions, we reorganize them into a…

This paper presents the theory of holomorphic vector valued modular forms from a geometric perspective. More precisely, we define certain holomorphic vector bundles on the modular orbifold of generalized elliptic curves whose sections are…

We consider the partition of a finite Coxeter group $W$ into left cells with respect to a weight function $L$. In the equal parameter case, Lusztig has shown that the representations carried by the left cells are precisely the so-called…

Borchers has shown that in a translation covariant vacuum representation of a theory of local observables with positive energy the following holds: The (Tomita) modular objects associated with the observable algebra of a fixed wedge region…

An algebraic classification is given for spaces of holomorphic vector-valued modular forms of arbitrary real weight and multiplier system, associated to irreducible, T-unitarizable representations of the full modular group, of dimension…

These notes are based on a course given at the EPFL in May 2005. It is concerned with the representation theory of Hecke algebras in the non-semisimple case. We explain the role that these algebras play in the modular representation theory…

We construct irreducible modules of centrally-extended classical Lie algebras over left ideals of the algebra of differential operators on the circle, through certain irreducible modules of centrally-extended classical Lie algebras of…

A modular form on an even lattice $M$ of signature $(l,2)$ is called reflective if it vanishes only on quadratic divisors orthogonal to roots of $M$. In this paper we show that every reflective modular form on a lattice of type $2U\oplus L$…

We give an integral representation of solutions of the elliptic Knizhnik-Zamolodchikov-Bernard equations for arbitrary simple Lie algebras. If the level is a positive integer, we obtain formulas for conformal blocks of the WZW model on a…

We construct, by contraction of a suitable complex vector bundle, the Weil representation of the finite symplectic group $Sp(A)$. We give an explicit description of the space of all lagrangian subspaces, which we use to compute the cocycle…

Let $p$ be a prime number and let $V$ be a continuous representation of $\mathrm{Gal}(\overline {\mathbf Q}/\mathbf Q)$ on a finite dimensional $\mathbf Q_p$-vector space, which is geometric. One of the Bloch-Kato conjectures for $V$…

We develop geometric methods to study the generating weights of free modules of vector valued modular forms of half-integral weight, taking values in a complex representation of the metaplectic group. We then compute the generating weights…

This article describes results of joint work with Michael Rapoport and Tonghai Yang. First, we construct an modular form \phi(\tau) of weight 3/2 valued in the arithmetic Chow group of the arithmetic surface M attached toa Shimura curve…

We use relative trace formula to prove a non-vanishing result and a subconvexity result for the twisted base change $L$-functions associated to Hilbert modular forms whose local components at ramified places are some supercuspidal…

We study meromorphic modular forms associated with positive definite binary quadratic forms and their cycle integrals along closed geodesics in the modular curve. We show that suitable linear combinations of these meromorphic modular forms…