Related papers: Antisymmetric Orbit Functions

Using the Schwinger-Keldysh-formalism, reformulated in arXiv:2108.01695 as an effective field theory in Euclidean anti-de Sitter, we evaluate the one-loop cosmological four-point function of a conformally coupled interacting scalar field in…

We study connections between the ring of symmetric functions and the characters of irreducible finite-dimensional representations of quantum affine algebras. We study two families of representations of the symplectic and orthogonal Lie…

The classification of the unitary irreducible representations of symmetry groups is a cornerstone of modern quantum physics, as it provides the fundamental building blocks for constructing the Hilbert spaces of theories admitting these…

A unified theory of quantum symmetric pairs is applied to q-special functions. Previous work characterized certain left coideal subalgebras in the quantized enveloping algebra and established an appropriate framework for quantum zonal…

In this paper, we describe the irreducible spherical functions of fundamental $K$-types associated with the pair $(G,K)=({\mathrm{SO}}(n+1),{\mathrm{SO}}(n))$ in terms of matrix hypergeometric functions. The output of this description is…

We define the symmetric (outer) automorphism group of a right-angled Artin group and construct for it a (spine of) Outer space. This `symmetric spine' is a contractible cube complex upon which the symmetric outer automorphism group acts…

We define a new basis of the algebra of quasi-symmetric functions by lifting the cycle-index polynomials of symmetric groups to noncommutative polynomials with coefficients in the algebra of free quasi-symmetric functions, and then…

We consider the nature of the wave function using the example of a harmonic oscillator. We show that the eigenfunctions $\psi_n{=}z^n$ of the quantum Hamiltonian in the complex Bargmann-Fock-Segal representation with $z\in\mathbb C$ are the…

In Part 1 we study the spherical functions on compact symmetric pairs of arbitrary rank under a suitable multiplicity freeness assumption and additional conditions on the branching rules. The spherical functions are taking values in the…

We prove a Cauchy identity for free quasi-symmetric functions and apply it to the study of various bases. A free Weyl formula and a generalization of the splitting formula are also discussed.

We give a new representation theoretic interpretation of the ring of quasi-symmetric functions. This is obtained by showing that the super analogue of the Gessel's fundamental quasi-symmetric function can be realized as the character of an…

The Weyl group of a crystallographic root system has a nonlinear action on the compact torus. The orbit space of this action is a compact basic semi-algebraic set. We present a polynomial description of this set for the Weyl groups of type…

Let $\mathfrak{g}$ be a complex semisimple Lie algebra and let $\mathbf{U}_q(\mathfrak{g})$ denote the associated Drinfel'd Jimbo quantized enveloping algebra. In this paper we study spherical functions of $\mathbf{U}_q(\mathfrak{g})$…

We note a remarkable similarity between the discretized Weyl-orbit functions and affine modular data associated with Wess-Zumino-Novikov-Witten (WZNW) conformal field theories. Known properties of the modular data are exploited here to…

Let $G\subset \O(n)$ be a group of isometries acting on $n$-dimensional Euclidean space $\R^n$, and ${\bf{X}}$ a bounded domain in $\R^n$ which is transformed into itself under the action of G. Consider a symmetric, classical…

Isotropic positive definite functions on spheres play important roles in spatial statistics, where they occur as the correlation functions of homogeneous random fields and star-shaped random particles. In approximation theory, strictly…

This is a survey article of geometric properties of noncommutative symmetric spaces of measurable operators $E(\mathcal{M},\tau)$, where $\mathcal{M}$ is a semifinite von Neumann algebra with a faithful, normal, semifinite trace $\tau$, and…

We put forward new explicit realisations of dS/CFT that relate ${\cal N}=2$ supersymmetric Euclidean vector models with reversed spin-statistics in three dimensions to specific supersymmetric Vasiliev theories in four-dimensional de Sitter…

We prove the equivalence of two conjectural constructions of unramified cuspidal automorphic functions on the adelic group GL_n(A) associated to an irreducible l-adic local system of rank n on an algebraic curve X over a finite field. The…

We consider composite functions in the elementary algebraic framework. Without any use of the Fourier transform, we find almost periodic orbits which suitably characterizes certain composite functions. In particular, we provide special…