Related papers: Symmetric differentials and jets extension of $L^2…

Let $\Sigma = \mathbb B^n/\Gamma$ be a complex hyperbolic space with discrete subgroup $\Gamma$ of the automorphism group of the unit ball $\mathbb B^n$ and $\Omega $ be a quotient of $\mathbb B^n \times\mathbb B^n$ under the diagonal…

This paper deals with the analytic continuation of holomorphic automorphic forms on a Lie group $G$. We prove that for any discrete subgroup $\Gamma$ of $G$ there always exists a non-trivial holomorphic automorphic form, i.e., there exists…

Let $M$ be a smooth manifold and $\Gamma$ a group acting on $M$ by diffeomorphisms; which means that there is a group morphism $\rho:\Gamma\rightarrow \mathrm{Diff}(M)$ from $\Gamma$ to the group of diffeomorphisms of $M$. For any such…

Let $X$ be a proper, non-compact CAT(-1) space, and $\Gamma$ a discrete cocompact subgroup of the isometries of $X$. We compactify the diagonal action of $\Gamma$ on $X \times X$ considering a domain of the horofunction boundary with…

Let $\widetilde{M}$ be a complex manifold and $\Gamma$ be a torsion-free cocompact lattice of $\text{Aut}(\widetilde{M})$. Let $\rho\colon\Gamma\to SU(N,1)$ be a representation and $M:=\widetilde M/\Gamma$ be an $n$-dimensional compact…

We prove the existence of a pair $(\Sigma ,\, \Gamma)$, where $\Sigma$ is a compact Riemann surface with $\text{genus}(\Sigma)\, \geq\, 2$, and $\Gamma\, \subset\, {\mathrm SL}(2, \mathbb C)$ is a cocompact lattice, such that there is a…

For a compact real form $U$ of a complex simple Lie group $G$, and an irreducible representation $\rho:\Gamma \to U$ of a Fuchsian group of the first kind $\Gamma$, it is shown that the classical isomorphism of Shimura, for the periods of a…

We study from an algebraic point of view the question of extending an action of a group \(\Gamma\) on a commutative domain \(R\) to a formal pseudodifferential operator ring \(B=R(\!(x\,;\,d)\!)\) with coefficients in \(R\), as well as to…

In this article we study the structure of $\Gamma$-invariant spaces of $L^2(\bf R)$. Here $\bf R$ is a second countable LCA group. The invariance is with respect to the action of $\Gamma$, a non commutative group in the form of a semidirect…

The purpose of this paper is to prove the long awaited holomorphy of the third symmetric power L-functions attached to nonmonomial cusp forms of GL_2 over an arbitrary number field on the whole complex plane.

In this paper, we introduce a unitary invariant $\Gamma$ defined on the unit ball of $B(H)^n$ in terms of the characteristic function, the noncommutative Poisson kernel, and the defect operator associated with a row contraction. We show…

We consider compact locally symmetric spaces $\Gamma\backslash G/H$ where $G/H$ is a non-compact semisimple symmetric space and $\Gamma$ is a discrete subgroup of $G$. We discuss some features of the joint spectrum of the (commutative)…

Dilaton gravities in two dimensions can be formulated as particular Poisson sigma models. Target space diffeomorphisms map different models to each other and establish a one-to-one correspondence between their classical solutions. We obtain…

In this paper, we investigate the $L^2$-Dolbeault cohomology of the symmetric power of cotangent bundles of ball quotients with finite volume, as well as their toroidal compactification. Through the application of Hodge theory for complete…

A symmetric function of $N$ variables can be given in terms of symmetric polynomials of these variables. We determine those symmetric polynomials in which the dual differential operators take the neatest form when expressed in terms of our…

We compute the cyclic homology for the cross-product al- gebra $A(M)\rtimes\Gamma$ of the algebra of complete symbols on a compact man- ifold $M$ with action of a finite group $\Gamma$. A spectral sequence argument shows that these groups…

The two-dimensional quantum harmonic oscillator is modified with reflection terms associated with the action of the Coxeter group $B_2$, which is the symmetry group of the square. The angular momentum operator is also modified with…

Let $\bold G$ be a reductive algebraic group defined over $\Q$, and let $\Gamma$ be an arithmetic subgroup of $\bold G(\Q)$. Let $X$ be the symmetric space for $\bold G(\R)$, and assume $X$ is contractible. Then the cohomology (mod torsion)…

The goal of the course was a review of results mainly due to M. Olbrich and the first author. We consider a discrete cocompact subgroup $\Gamma$ of a semisimple Lie group $G$. We relate the group cohomology of $\Gamma$ with coefficients in…

Let $M$ be a smooth manifold. When $\Gamma$ is a group acting on the manifold $M$ by diffeomorphisms one can define the $\Gamma$-co-invariant cohomology of $M$ to be the cohomology of the differential complex…