Related papers: Fundamental quasisymmetric functions in superspace

We report general properties of N-fold supersymmetry in one-dimensional quantum mechanics. N-fold supersymmetry is characterized by supercharges which are N-th polynomials of momentum. Relations between the anti-commutator of the…

We begin by defining general hypergeometric functions over finite fields and obtaining a finite field analogue of a classical symmetry in their complex counterparts. We give a geometric proof for the symmetry by constructing isomorphisms…

We introduce a new pair of mutually dual bases of noncommutative symmetric functions and quasi-symmetric functions, and use it to derive generalizations of several results on the reduced incidence algebra of the lattice of noncrossing…

We establish general versions of a variety of results for quasiconvex, lower-semicontinuous, and law-invariant functionals. Our results extend well-known results from the literature to a large class of spaces of random variables. We…

An identity is derived expressing Schur functions as sums over products of pairs of Schur $Q$-functions, generalizing previously known special cases. This is shown to follow from their representations as vacuum expectation values (VEV's) of…

First we extend the theory of subharmonic functions on smooth strictly $k$-analytic curves from Thuillier's thesis to the case of possibly singular analytic curves over a non-archimedean field. Classically psh functions are then defined as…

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…

This work deals with function theory on quantum complex hyperbolic spaces. The principal notions are expounded. We obtain explicit formulas for invariant integrals on `finite' functions on a quantum hyperbolic space and on the associated…

Egge, Loehr and Warrington gave in \cite{ELW} a combinatorial formula that permits to convert the expansion of a symmetric function, homogeneous of degree $n$, in terms of Gessel's fundamental quasisymmetric functions into an expansion in…

Attention is focused on antisymmetrised versions of quantum spaces that are of particular importance in physics, i.e. Manin plane, q-deformed Euclidean space in three or four dimensions as well as q-deformed Minkowski space. For each of…

The formalism of Supersymmetric Quantum Mechanics provides us the eigenfunctions to be used in the variational mathod to obtain the eigenvalues for the Hulth\'en Potential.

A production function $f$ is called quasi-sum if there are strict monotone functions $F, h_1,...,h_n$ with $F'>0$ such that $$f(x)= F(h_1 (x_1)+...+h_n (x_n)).$$ The justification for studying quasi-sum production functions is that these…

We discover a modular property of supersymmetric partition functions of supersymmetric theories with R-symmetry in four dimensions. This modular property is, in a sense, the generalization of the modular invariance of the supersymmetric…

The quasisymmetric generating function of the set of permutations whose inverses have a fixed descent set is known to be symmetric and Schur-positive. The corresponding representation of the symmetric group is called the descent…

Multi-Schur functions are symmetric functions that generalize the supersymmetric Schur functions, the flagged Schur functions, and the refined dual Grothendieck functions, which have been intensively studied by Lascoux. In this paper, we…

We study the quantum symmetric spaces for quantum general linear groups modulo symplectic groups. We first determine the structure of the quotient quantum group and completely determine the quantum invariants. We then derive the…

The classical action of a two dimensional N=2 supersymmetric theory, characterized by a general K\"{a}hler potential, is written down on a non(anti)commutative superspace. The action has a power series expansion in terms of the determinant…

We formulate N-fold supersymmetry in quantum mechanical matrix models. As an example, we construct general two-by-two Hermitian matrix 2-fold supersymmetric quantum mechanical systems. We find that there are two inequivalent such systems,…

We analyze general structure of N-fold supersymmetry which provides a systematic framework to construct weakly quasi-solvable quantum mechanical systems. Main ingredients of our analysis are dimensional analysis and introduction of an…

Space-time multivectors in Clifford algebra (space-time algebra) and their application to nonlinear electrodynamics are considered. Functional product and infinitesimal operators for translation and rotation groups are introduced, where…