Related papers: On Einstein Structures for $\mathrm{SO}_0(p,p+1)$-…

For a $p$-adic field $F$, the space of pro-$p$-Iwahori invariants of a universal supersingular mod $p$ representation $\tau$ of ${\rm GL}_2(F)$ is determined in the works of Breuil, Schein, and Hendel. The representation $\tau$ is…

Explicit models for the restricted conformal group of the Einstein static universe of dimension greater than two and for its universal covering group are constructed. Based on these models, as an application we determine all oriented and…

We will discuss fundamental domains for actions of discrete groups on the 3-dimensional Einstein Universe. These will be bounded by crooked surfaces, which are conformal compactifications of surfaces that arise in the construction of…

This paper is devoted to the representations of the groups $SO (2,1)$ and $ISO (2,1)$. Those groups have an important role in cosmology, elementary particle theory and mathematical physics. Irreducible unitary representations of the…

Given a continuous, odd, reducible and semi-simple $2$-dimensional representation $\bar\rho_0$ of $G_{\mathbb{Q},Np}$ over a finite field of odd characteristic $p$, we study the relation between the universal deformation ring of the…

In this article, we study the problem of the existence and nonexistence of warping function associated with constant scalar curvature on pseudo-Riemannian Poisson warped product space under the assumption that fiber space has constant…

Let G be a connected, compact, semisimple Lie group. It is known that for a compact closed orientable surface $\Sigma$ of genus $l >1$, the order of the group $H^2(\Sigma,\pi_1(G))$ is equal to the number of connected components of the…

The energy of harmonic sections of flat bundles of nonpositively curved (NPC) length spaces over a Riemann surface $S$ is a function $E_\rho$ on Teichm\"uller space $\Teich$ which is a qualitative invariant of the holonomy representation…

We study unitarity of the induced representations from coisotropic quantum subgroups which were introduced in math.QA/9804138. We define a real structure on coisotropic subgroups which determines an involution on the homogeneous space. We…

Let $S$ be a closed Riemann surface of genus $g \geq 2$ and $\varphi$ be a conformal automorphism of $S$, of prime order $p$ such that $S/\langle \varphi \rangle$ has genus zero. Let ${\mathbb K} \leq {\mathbb C}$ be a field of definition…

We compactify M(atrix) theory on Riemann surfaces Sigma with genus g>1. Following [1], we construct a projective unitary representation of pi_1(Sigma) realized on L^2(H), with H the upper half-plane. As a first step we introduce a suitably…

In their construction of the topological index for flat vector bundles, Atiyah, Patodi and Singer associate to each flat vector bundle a particular $\mathbb{C/Z}$-$K$-theory class. This assignment determines a map, up to weak homotopy, from…

We analyze the hamiltonian quantization of Chern-Simons theory associated to the universal covering of the Lorentz group SO(3,1). The algebra of observables is generated by finite dimensional spin networks drawn on a punctured topological…

Let $(\pi, \mathcal H)$ be a continuous unitary representation of the (infinite dimensional) Lie group $G$ and $\gamma \: \mathbb R \to \mathrm{Aut}(G)$ define a continuous action of $\mathbb R$ on $G$. Suppose that $\pi^\#(g,t) = \pi(g)…

The compact groups such as $SU(n)$ and $SO(n)$ groups have been heavily studied and applied in the study of quantum many body systems. However, the non-compact groups such as the real symplectic groups are less touched. In this paper, we…

We consider a locally trivial fiber bundle $\pi : E \to M$ over a compact oriented two-dimensional manifold $M$, and a section $s$ of this bundle defined over $M \setminus \Sigma$, where $\Sigma$ is a discrete subset of $M$. We call the set…

We study the structure of the spectrum of the algebra of uniformly continuous holomorphic functions on the unit ball of $\ell_p$. Our main focus is the relationship between \emph{Gleason parts} and \emph{fibers}. For every $z \in…

Throughout the history of Einstein manifolds, differential geometers have shown great interest in finding the relationships between curvature and the topology of Einstein manifolds. In the paper, first, we prove that a compact Einstein…

We investigate the representation theory of the polynomial core of the quantum Teichmuller space of a punctured surface S. This is a purely algebraic object, closely related to the combinatorics of the simplicial complex of ideal cell…

Let $S$ be a punctured surface of negative Euler characteristic. We show that given a generic representation $\rho:\pi_1(S) \rightarrow \mathrm{PSL}_n(\mathbb{C})$, there exists a positive representation $\rho_0:\pi_1(S) \rightarrow…