Related papers: Cusped Borel Anosov representations with positivit…

The main question we are going to address in this paper is: How much does the representation theory of the $p$-adic group $\mathrm{GL}_n(\mathcal{D})$ depend on the $p$-adic division algebra $\mathcal{D}$? Let $\mathcal{D}$ be a central…

Let $G$ be a connected semisimple real algebraic group and $\Gamma$ a Zariski dense Anosov subgroup of $G$ with respect to a minimal parabolic subgroup $P$. Let $N$ be the maximal horospherical subgroup of $G$ given by the unipotent radical…

In this paper we complete the topological description of the space of representations of the fundamental group of a punctured surface in SL(2,R) with prescribed behavior at the punctures and nonzero Euler number, following the strategy…

A $\gamma$-deformed version of $\mathfrak{su}(2)$ algebra has been obtained from a bi-orthogonal system of vectors in $\bf{C^2}$. Fusion of Jordan-Schwinger realization of complexified $\mathfrak{su}(2)$ with Dyson-Maleev representation…

Let $V$ be an irreducible representation of group $GL_n({\mathbb C})$, which appears as a submodule in $({\mathbb C}^n)^{\otimes d}$, where ${\mathbb C}^n$ is the tautological $n$-dimensional representation of $GL_n$, and $d$ is a…

The comultiplication formula for fusion products of untwisted representations of the chiral algebra is generalised to include arbitrary twisted representations. We show that the formulae define a tensor product with suitable properties, and…

This paper is concerned with the Vlasov-Poisson-Boltzmann system for plasma particles of two species in three space dimensions. The Boltzmann collision kernel is assumed to be angular non-cutoff with $-3<\gamma<-2s$ and $1/2\leq s<1$, where…

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…

Let $e$ denote the Euler class on the space $Hom(\Gamma_g, PSL(2,\mathbb R))$ of representations of the fundamental group $\Gamma_g$ of the closed surface $\Sigma_g$ of genus $g$. Goldman showed that the connected components of…

In arXiv:1403.7671, Kapovich, Leeb and Porti gave several new characterizations of Anosov representations $\Gamma \to G$, including one where geodesics in the word hyperbolic group $\Gamma$ map to "Morse quasigeodesics" in the associated…

The supercharacter theory of algebra groups gave us a representation theoretic realization of the Hopf algebra of symmetric functions in noncommuting variables. The underlying representation theoretic framework comes equipped with two…

Given an almost unimodular $G$, so that the Plancherel weight $\varphi_G$ on the group von Neumann algebra $L(G)$ is almost periodic, we show that the basic construction for the inclusion $L(G)^{\varphi_G} \leq L(G)$ is isomorphic to a…

The aim of this note is to advertise on a result, not stated explicitly, but proved, in arXiv:0802.0512. Namely, if $\Gamma$ is any group, if $\rho_1$, $\rho_2$ are representations of $\Gamma$ in $\mathrm{PSL}(2,\mathbb{R})$, one of them…

We say that two unitary or orthogonal representations of a finitely generated group $G$ are additive conjugates if they are intertwined by an additive map, which need not be continuous. We associate to each representation of $G$ a…

In the case of smooth non-invertible maps which are hyperbolic on folded basic sets $\Lambda$, we give approximations for the Gibbs states (equilibrium measures) of arbitrary H\"{o}lder potentials, with the help of weighted sums of atomic…

Let $\Delta=\Delta_1\times\ldots\times \Delta_d\subseteq\mathbb{R}^n$, where $\mathbb{R}^n=\mathbb{R}^{n_1}\times\cdots\times\mathbb{R}^{n_d}$ with each $\Delta_i\subseteq\mathbb{R}^{n_i}$ a non-degenerate simplex of $n_i$ points. We prove…

Lorentz's group represented by the hypercomplex system of numbers, which is based on dirac matrices, is investigated. This representation is similar to the space rotation representation by quaternions. This representation has several…

The Kazakov-Migdal model, if considered as a functional of external fields, can be always represented as an expansion over characters of $GL$ group. The integration over "matter fields" can be interpreted as going over the {\it model} (the…

We investigate the characters of some finite-dimensional representations of the quantum affine algebras $U_q(\hat{g})$ using the action of the copy of $U_q(g)$ embedded in it. First, we present an efficient algorithm for computing the…

All irreducible representations of the Chinese monoid $C_n$, of any rank $n$, over a nondenumerable algebraically closed field $K$, are constructed. It turns out that they have a remarkably simple form and they can be built inductively from…