ﻻ يوجد ملخص باللغة العربية
We provide elementary identities relating the three known types of non-symmetric interpolation Macdonald polynomials. In addition we derive a duality for non-symmetric interpolation Macdonald polynomials. We consider some applications of these results, in particular for binomial formulas involving non-symmetric interpolation Macdonald polynomials.
We give a new sufficient condition on a spectral triple to ensure that the quantum group of orientation and volume preserving isometries defined in cite{qorient} has a $C^*$-action on the underlying $C^*$ algebra.
Two criteria for planarity of a Feynman diagram upon its propagators (momentum flows) are presented. Instructive Mathematica programs that solve the problem and examples are provided. A simple geometric argument is used to show that while one can pla
We have two constructions of the level-$(0,1)$ irreducible representation of the quantum toroidal algebra of type $A$. One is due to Nakajima and Varagnolo-Vasserot. They constructed the representation on the direct sum of the equivariant K-groups of
We discuss a generalization of the conditions of validity of the interpolation method for the density of quenched free energy of mean field spin glasses. The condition is written just in terms of the $L^2$ metric structure of the Gaussian random vari
In the 90s a collection of Plethystic operators were introduced in [3], [7] and [8] to solve some Representation Theoretical problems arising from the Theory of Macdonald polynomials. This collection was enriched in the research that led to the resul