相关论文: Crossratios, Surface Groups, SL(n,R) and C^{1}(S^1…

We give a complete list of the one-dimensional groups definable in algebraically closed valued fields and i the pseudo-local fields, up to a finite index subgroup and a quotient by a finite subgroup.

The SL(3,C)-representation variety R of a free group F arises naturally by considering surface group representations for a surface with boundary. There is a SL(3,C)-action on the coordinate ring of R by conjugation. The geometric points of…

Though the uniformization theorem guarantees an equivalence of Riemann surfaces and smooth algebraic curves, moving between analytic and algebraic representations is inherently transcendental. Our analytic curves identify pairs of circles…

We generalise surface cluster algebras to the case of infinite surfaces where the surface contains finitely many accumulation points of boundary marked points. To connect different triangulations of an infinite surface, we consider infinite…

We construct embeddings of surface groups into the group of germs of analytic diffeomorphisms in one variable.

We show that certain classes of graphs of free groups contain surface subgroups, including groups with positive $b_2$ obtained by doubling free groups along collections of subgroups, and groups obtained by "random" ascending HNN extensions…

We introduce an infinite-dimensional affine group and construct its irreducible unitary representation. Our approach follows the one used by Vershik, Gelfand and Graev for the diffeomorphism group, but with modifications made necessary by…

We show the irreducibility of some unitary representations of the group of symplectomorphisms and the group of contactomorphisms.

If G is a (connected) complex Lie Group and Z is a generalized flag manifold for G, the the open orbits D of a (connected) real form G_0 of G form an interesting class of complex homogeneous spaces, which play an important role in the…

The group $SO(d+1,1)$ makes an appearance both as the conformal group of Euclidean space in $d$ dimensions and as the isometry group of de Sitter spacetime in $d+1$ dimensions. While this common feature can be taken as a hint towards…

We generalise in this article the Mc Shane-Mirzakhani identities in hyperbolic geometry to arbitrary cross ratios. We give an expression of them in the case of Hitchin representations of surface groups in PSL(n, R) in a suitable choice of…

We describe the structure of the irreducible representations of crossed products of unital C*-algebras by actions of finite groups in terms of irreducible representations of the C*-algebras on which the groups act. We then apply this…

In this paper, we develop a representation-theoretic formulation of discrete-time linear systems. We show that such systems are naturally viewed as representations of time groups acting on vector spaces, thereby endowing the state space…

We study representations of $GL_{n}(\mathbb{F}_{q})$ that are distinguished with respect to a symmetric subgroup $H=GL_{n}(\mathbb{F}_{q})^{\sigma}$, where $\sigma$ is an involution. We prove that those representations satisfy $\pi \cong…

We give a local representation for the pseudoholomorphic surfaces in Euclidean spheres in terms of holomorphic data. Similar to the case of the generalized Weierstrass representation of Hoffman and Osserman, we assign such a surface in…

We address a linearity problem for differentiable vectors in representations of infinite-dimensional Lie groups on locally convex spaces, which is similar to the linearity problem for the directional derivatives of functions.

A triangle group is denoted by $\Delta(p,q,r)$ and has finite presentation $$ \Delta(p,q,r)=\langle x,y | x^p=y^q=(xy)^r=1 \rangle .$$ We examine a method for composition of permutation representations of a triangle group $\Delta(p,q,r)$…

We give a new proof of a theorem of D. Calegari that says that the Cayley graph of a surface group with respect to any generating set lying in finitely many mapping class group orbits has infinite diameter. This applies, for instance, to…

We prove a global topological rigidity theorem for locally $C^2$-non-discrete subgroups of the group of real analytic diffeomorphisms of the circle.

In this lecture, we survey a number of recent results and developments regarding the representation theory of infinite-dimensional quantum groups (quantum affine algebras and related algebras), as well as their connections with cluster…