Related papers: Poisson transform and unipotent complex geometry

We give a construction of a Poisson transform mapping density valued differential forms on generalized flag manifolds to differential forms on the corresponding Riemannian symmetric spaces, which can be described entirely in terms of finite…

Utilizing the theory of the Poisson transform, we develop some new concrete models for the Hecke theory in a space $M_{\lambda}(N)$ of Maass forms with eigenvalue $1/4-\lambda^2$ on a congruence subgroup $\Gamma_1(N)$. We introduce the…

Let $\,G/K\,$ be a non-compact irreducible Hermitian symmetric space of rank $\,r\,$ and let $\,NAK\,$ be an Iwasawa decomposition of $\,G$. By the polydisc theorem, $\,AK/K\,$ can be regarded as the base of an $\,r$-dimensional tube domain…

We develop a structure theory for transposed Poisson algebras over fields of characteristic different from two. In particular, we prove that every finite-dimensional transposed Poisson algebra over an algebraically closed field decomposes…

Let \(X=G/K\) be a noncompact complex Grassmann manifold of rank \(r\). Let \(\tau_l\) be a character of \(K\), \(G\times_P{\C}\) and \(G\times_K{\C}\) the homogeneous line bundles associated with the representations…

The semiclassical limit of full non-commutative gauge theory is known as Poisson gauge theory. In this work we revise the construction of Poisson gauge theory paying attention to the geometric meaning of the structures involved and advance…

Let $\Omega=G/K$ be a bounded symmetric domain and $S=K/L$ its Shilov boundary. We consider the action of $G$ on sections of a homogeneous line bundle over $\Omega$ and the corresponding eigenspaces of $G$-invariant differential operators.…

Let $G$ be a semisimple Lie group with finite center, $K\subset G$ a maximal compact subgroup, and $P\subset G$ a parabolic subgroup. Following ideas of P.Y.\ Gaillard, one may use $G$-invariant differential forms on $G/K\times G/P$ to…

On a compact connected group $G$, consider the infinitesimal generator $-L$ of a central symmetric Gaussian convolution semigroup $(\mu_t)_{t>0}$. We establish several regularity results of the solution to the Poisson equation $LU=F$, both…

We characterize the image of the Poisson transform on any distinguished boundary of a Riemannian symmetric space of the noncompact type by a system of differential equations. The system corresponds to a generator system of a two sided…

We investigate some genuine Poisson geometric objects in the modular theory of an arbitrary von Neumann algebra $\mathfrak{M}$. Specifically, for any standard form realization $(\mathfrak{M},\mathcal{H},J,\mathcal{P})$, we find a canonical…

Let L be a Lie group and Lambda a lattice in L. Suppose G is a non-compact simple Lie group realized as a Lie subgroup of L, and the image of G on L/Lambda is dense. Let c be a diagonalizable element of G not contained in a compact…

We study invariant Nijenhuis $(1,1)$-tensors on a homogeneous space $G/K$ of a reductive Lie group $G$ from the point of view of integrability of a Hamiltonian system of differential equations with the $G$-invariant Hamiltonian function on…

We introduce C-Algebras of compact Riemann surfaces $\Sigma$ as non-commutative analogues of the Poisson algebra of smooth functions on $\Sigma$. Representations of these algebras give rise to sequences of matrix-algebras for which…

Let $(G,\kappa)$ be a compact connected Lie group endowed with a biinvariant Riemannian metric, and let $\tilde{G}$ be the complexification of $G$. We apply Grauert tube techniques to the near-diagonal scaling asymptotics of certain…

The Zak transform on $\mathbb{R}^d$ is an important tool in condensed matter physics, signal processing, time-frequency analysis, and harmonic analysis in general. This article introduces a generalization of the Zak transform to a class of…

In this paper, we present a theory of Poisson deformation of Hamiltonian quasi-Poisson manifolds to Hamiltonian Poisson manifolds that include degenerate cases. More significantly, this theory extends to singular cases arising from…

We demonstrate the common bihamiltonian nature of several integrable systems. The first one is an elliptic rotator that is an integrable Euler-Arnold top on the complex group GL(N) for any $N$, whose inertia ellipsiod is related to a choice…

We construct the moduli spaces associated to the solutions of equations of motion (modulo gauge transformations) of the Poisson sigma model with target being an integrable Poisson manifold. The construction can be easily extended to a case…

Let G be the group of all formal power series starting with x with coefficients in a field k of zero characteristic (with the composition product), and let F[G] be its function algebra. C. Brouder and A. Frabetti introduced a…