Related papers: Discrete series Whittaker functions on $Spin(2n,2)…
In this paper, we study the Whittaker modules for the quantum enveloping algebra $U_q(\sl_3)$ with respect to a fixed Whittaker function. We construct the universal Whittaker module, find all its Whittaker vectors and investigate the…
We study N=1,2,4 higher spin superalgebras in four dimensions and higher spin gauge theories based on them. We extend the existing minimal N=2,4 theories and find a minimal N=1 theory. Utilizing the basic structure of the minimal N=8…
This paper is devoted to constructing and studying exactly solvable dynamical systems in discrete time obtained from some algebraic operations on matrices, to reductions of such systems leading to classical field theory models in…
We present a family of unitary irreducible representations of SU(2) realized in the plane, in terms of the Laguerre polynomials. These functions are similar to the spherical harmonics defined on the sphere. Relations with an space of square…
In this paper we tackle a question raised by N. Templier and A. Saha concerning the size of Whittaker new vectors appearing in infinite dimensional representations of GL(2) over non-archimedean fields. We derive precise bounds for such…
In this paper, following a similar procedure developed by Buttcane and Miller in \cite{MillerButtcane} for $SL(3,\RR)$, the $(\frakg,K)$-module structure of the minimal principal series of real reductive Lie groups $SU(2,1)$ is described…
The algebra of differential geometry operations on symmetric tensors over constant curvature manifolds forms a novel deformation of the sl(2,R) [semidirect product] R^2 Lie algebra. We present a simple calculus for calculations in its…
The affine Weyl groups with their corresponding four types of orbit functions are considered. Two independent admissible shifts, which preserve the symmetries of the weight and the dual weight lattices, are classified. Finite subsets of the…
We perform Monte Carlo simulations of 2-d dynamically triangulated surfaces coupled to Ising and three--states Potts model matter. By measuring spin-spin correlation functions as a function of the geodesic distance we provide substantial…
Let S be a flat surface of genus g with cone type singularities. Given a bipartite graph G isoradially embedded in S, we define discrete analogs of the 2^{2g} Dirac operators on S. These discrete objects are then shown to converge to the…
The $SL(3)$ Kuznetsov formula exists in several versions, and has been employed with some success to study automorphic forms on $SL(3)$. In each version, the weight functions on the geometric side are given by multiple integrals with…
We extend the notion of generalized Whittaker models by allowing them to be built upon smooth irreducible representations of unipotent subgroups of a $p$-adic reductive group that are not necessarily characters, nor induced from Weil…
We introduce gauge networks as generalizations of spin networks and lattice gauge fields to almost-commutative manifolds. The configuration space of quiver representations (modulo equivalence) in the category of finite spectral triples is…
We demonstrate a fast spin-s spherical harmonic transform algorithm, which is flexible and exact for band-limited functions. In contrast to previous work, where spin transforms are computed independently, our algorithm permits the…
For a family of integer-valued height functions defined over the faces of planar graphs, we establish a relation between the probability of connection by level sets and the spin-spin correlations of the dual $O(2)$ symmetric spin models…
We introduce a numerical method for reconstructing a multidimensional surface using the gradient of the surface measured at some values of the coordinates. The method consists of defining a multidimensional spline function and minimizing…
This paper proposes semi-discrete and fully discrete hybridizable discontinuous Galerkin (HDG) methods for the Burgers' equation in two and three dimensions. In the spatial discretization, we use piecewise polynomials of degrees $ k \ (k…
We study the Harmonic and Dirac Oscillator problem extended to a three-dimensional noncom- mutative space where the noncommutativity is induced by a shift of the dynamical variables with generators of SL(2;R) in a unitary irreducible…
We set up the conventional conformal bootstrap equations in Mellin space and analyse the anomalous dimensions and OPE coefficients of large spin double trace operators. By decomposing the equations in terms of continuous Hahn polynomials,…
The functional determinants of the GJMS scalar operators, P_{2k}, on even-dimensional spheres are computed via Barnes multiple gamma functions relying on the numerical availability of the digamma function. For the critical k=d/2 case, it is…