Related papers: Minimal representations: spherical vectors and aut…

We consider discrete minimal surface algebras (DMSA) as generalized noncommutative analogues of minimal surfaces in higher dimensional spheres. These algebras appear naturally in membrane theory, where sequences of their representations are…

We give a pedagogical survey of those aspects of the abstract representation theory of quantum groups which are related to the Tannaka-Krein reconstruction problem. We show that every concrete semisimple tensor *-category with conjugates is…

The Weil representation is used to construct a minimal type of the two-fold central extension of $\operatorname{Sp}_{2n}(\mathbb{Q}_2)$. The corresponding Hecke algebra is shown to be isomorphic to the classical affine Hecke algebra of the…

Contents: Rational functions with given monodromy on generic curves (I. Bouw & S. Wewers); Can deformation rings of group representations not be local complete intersections? (T. Chinburg); Lifting an automorphism group to finite…

Matrix elements and spherical functions of irreducible representations of the de Sitter group are studied on the various homogeneous spaces of this group.

We classify non-polar irreducible representations of connected compact Lie groups whose orbit space is isometric to that of a representation of a finite extension of $Sp(1)^k$ for some $k>0$. It follows that they are obtained from isotropy…

We investigate the representation theory of the rational and trigonometric Cherednik algebra of type $GL_n$ by means of combinatorics on periodic (or cylindrical) skew diagrams. We introduce and study standard tableaux and plane partitions…

We prove delocalization of eigenvectors of vertex-transitive graphs via elementary estimates of the spectral projector. We recover in this way known results which were formerly proved using representation theory. Similar techniques show…

We analyze the abstract representations of the groups of rational points of even-dimensional quasi-split special unitary groups associated with quadratic field extensions. We show that, under certain assumptions, such representations have a…

The aim of this paper is to study the virtual classes of representation varieties of surface groups onto the rank one affine group. We perform this calculation by three different approaches: the geometric method, based on stratifying the…

We construct a symplectic, globally defined, minimal-coordinate, equivariant integrator on products of 2-spheres. Examples of corresponding Hamiltonian systems, called spin systems, include the reduced free rigid body, the motion of point…

A minimal representation of a simple non-compact Lie group is obtained by ``quantizing'' the minimal nilpotent coadjoint orbit of its Lie algebra. It provides context for Roger Howe's notion of a reductive dual pair encountered recently in…

We introduce and study a new class of representations of surface groups into Lie groups of Hermitian type, called weakly maximal representations. They are defined in terms of invariants in bounded cohomology and extend considerably the…

This book is mainly an exposition of the author's works and his joint works with his former students on explicit representations of finite-dimensional simple Lie algebras, related partial differential equations, linear orthogonal algebraic…

The representation theory of semisimple algebraic groups over the complex numbers (equivalently, semisimple complex Lie algebras or Lie groups, or real compact Lie groups) and the question of whether a given representation is symplectic or…

Let G be a semisimple almost simple algebraic group defined and split over a nonarchimedean local field K and let V be a unipotent representation of G(K) (for example, an Iwahori-spherical representation). We calculate the character of V at…

We study minimal Lagrangian surfaces in the complex hyperbolic quadric. We show that minimality of a Lagrangian surface is characterized by a loop of flat connections, which yields an associated $\mathbb S^1$-family of isometric…

We study the automorphism group of the algebraic closure of a substructure A of a pseudo-finite field F, or more generally, of a bounded PAC field F. This paper answers some of the questions of [1], and in particular that any finite group…

We classify the irreducible projective representations of symmetric and alternating groups of minimal possible and second minimal possible dimensions, and get a lower bound for the third minimal dimension. On the way we obtain some new…

We introduce and study \emph{simple Anosov representations} of closed hyperbolic surface groups, analogous to Minsky's \emph{primitive stable representations} of free groups. We prove that the set of simple Anosov representations into…