Related papers: Representation formula for discrete indefinite aff…
We study finite dimensional representations of the projective modular group. Various explicit dimension formulas are given.
We construct discrete and faithful representations into the isometry group of a hyperbolic space of the fundamental groups of acute negatively curved even-sided polygons of finite groups.
We introduce an infinite-dimensional $p$-adic 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…
We introduce and study the so-called serpentine representations of the infinite symmetric group $\sinf$, which turn out to be closely related to the basic representation of the affine Lie algebra $\widehat{\mathfrak{sl}_2}$ and…
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…
We investigate representations of mapping class groups of surfaces that arise from the untwisted Drinfeld double of a finite group G, focusing on surfaces without marked points or with one marked point. We obtain concrete descriptions of…
In this paper, we characterize unitary representations of the fundamental group of a punctured sphere whose generators can be decomposed into products of two Lagrangian involutions. Our main result is that such representations are exactly…
We classify all regular three-dimensional convex cones which possess an automorphism group of dimension at least two, and provide analytic expressions for the complete hyperbolic affine spheres which are asymptotic to the boundaries of…
We construct highly singular projective curves and surfaces defined by invariants of primitive complex reflection groups.
By analogy with the real and complex affine groups, whose unitary irreducible representations are used to define the one and two-dimensional continuous wavelet transforms, we study here the quaternionic affine group and construct its…
Birkhoff's representation theorem (Birkhoff, 1937) defines a bijection between elements of a distributive lattice and the family of upper sets of an associated poset. Although not used explicitly, this result is at the backbone of the…
An algorithm for irreducible decomposition of representations of finite groups over fields of characteristic zero is described. The algorithm uses the fact that the decomposition induces a partition of the invariant inner product into a…
We prove a Mackey formula for representations of finite groups of Lie type, in the case where the groups come from disconnected reductive groups.
We will first clarify the loop group formulations for both hyperbolic and elliptic definite affine spheres in R^3. Then we classify the rational elements with 3 poles or 6 poles in a real twisted loop group, and compute dressing actions of…
For $S$ a closed surface of genus at least $2$, let $\mathrm{Hit}_3(S)$ be the Hitchin component of representations to $\mathrm{SL}(3,\mathbb{R}),$ equipped with the Labourie-Loftin complex structure. We construct a mapping class group…
The Hermite-Birkhoff interpolation problem of a function given on arbitrarily distributed points on the sphere and other manifolds is considered. Each proposed interpolant is expressed as a linear combination of basis functions, the…
We construct the representations of affine sl(2,R) starting from the unitary representations of the loop ax+b-group. Our approach involves a combinatorial analysis of the correlation functions of the generators and renormalization of the…
We demonstrate the main idea of constructing irreducible unitary representations of Lie groups by using Fedosov deformation quantization in the concrete case of the group Aff(R) of affine transformations of the real straight line. By an…
We present a classification of all spherical indecomposable representations of classical and exceptional Lie superalgebras. We also include information about stabilizers, symmetric algebras, and Borels for which sphericity is achieved. In…
For an affine double plane defined by an equation of the form z^2 = f, we study the divisor class group and the Brauer group. Two cases are considered. In the first case, f is a product of n linear forms in k[x,y] and X is birational to a…