Related papers: Super-Whittaker vector at c=3/2
We formalize the notion of vector semi-inner products and introduce a class of vector seminorms which are built from these maps. The classical Pythagorean theorem and parallelogram law are then generalized to vector seminorms that have a…
This paper is concerned with a link between central extensions of N=2 superconformal algebra and a supersymmetric two-component generalization of the Camassa--Holm equation. Deformations of superconformal algebra give rise to two compatible…
Vogel's universality implies a unified description of the adjoint sector of representation theory for simple Lie algebras in terms of three parameters $\alpha,\beta,\gamma$, which are homogeneous coordinates of Vogel's plane. Actually this…
To prove that a measure, linearly representable by means of a finite set of nonnegative matrices $\mathcal M$, has the weak-Gibbs property, one check the uniform convergence (on $\mathcal M^\mathbb N$) of the sequence of vectors…
The two-parametric quantum superalgebra $U_{pq}[gl(2/2)]$ and its representations are considered. All finite-dimensional irreducible representations of this quantum superalgebra can be constructed and classified into typical and nontypical…
Recently a remarkable map between 4-dimensional superconformal field theories and vertex algebras has been constructed \cite{BLLPRV15}. This has lead to new insights in the theory of characters of vertex algebras. In particular it was…
In this article, we give an explicit construction of the simple modules for both non-degenerate and degenerate cyclotomic Hecke-Clifford superalgebras over an algebraically closed field of characteristic not equal to $2$ under certain…
In this paper we establish a connection between the associated variety of a representation and the existence of certain degenerate Whittaker functionals, for both smooth and K-finite vectors, for all quasi-split real reductive groups,…
Torsion polynomials connect the genus of a hyperbolic knot (a topological invariant) with the discrete faithful representation (a geometric invariant). Using a new combinatorial structure of an ideal triangulation of a 3-manifold that…
We show that, for an arbitrary quasi-reductive Lie superalgebra with a triangular decomposition and a character $\zeta$ of the nilpotent radical, the associated Backelin functor $\Gamma_\zeta$ sends Verma modules to standard Whittaker…
In this paper, we will study the deformation of a three dimensional theory with $\mathcal{N} =2$ supersymmetry. This theory will be deformed by the presence of a constant vector field. This deformation will break the Lorentz symmetry. So,…
We show that the symmetry operators for the quantum superintegrable system on the 3-sphere with generic 4-parameter potential form a closed quadratic algebra with 6 linearly independent generators that closes at order 6 (as differential…
We study Whittaker vectors (and Jacquet integrals) in the generalized principal series for a real reductive group. A functional equation for them is obtained. This allows to establish uniform estimates for their holomorphic extensions with…
Symmetric Jack polynomials arise naturally in several contexts, including statistics, physics, combinatorics, and representation theory. They are pairwise orthogonal with repsect to two different inner products, the first defined by…
We develop a theory of Jacobi polynomials for parabolic subgroups of finite reflection groups that specializes to the cases studied by Heckman and Opdam in which the whole group and the trivial group are considered. For the intermediate…
We analyze conditions under which a projection from the vector-valued Jack or Macdonald polynomials to scalar polynomials has useful properties, especially commuting with the actions of the symmetric group or Hecke algebra, respectively,…
AGT correspondence gives an explicit expressions for the conformal blocks of $d=2$ conformal field theory. Recently an explanation of this representation inside the CFT framework was given through the assumption about the existence of the…
The theory of symmetric functions has been extended to the case where each variable is paired with an anticommuting one. The resulting expressions, dubbed superpolynomials, provide the natural N=1 supersymmetric version of the classical…
A superintegrable finite model of the quantum isotropic oscillator in two dimensions is introduced. It is defined on a uniform lattice of triangular shape. The constants of the motion for the model form an SU(2) symmetry algebra. It is…
We determine the coefficient of proportionality between two multidimensional hypergeometric integrals. One of them is a solution of the dynamical difference equations associated with a Young diagram and the other is the vertex integral…