Related papers: Paths, Demazure Crystals and Symmetric Functions
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…
Multiple-integral representations of the (skew-)Macdonald symmetric functions are obtained. Some bosonization schemes for the integral representations are also constructed.
In this paper we discuss approximation of partially smooth functions. The problem arises naturally in the study of laminated currents.
Given recipe of qualitative, kinetic modelling by geometric methods of three-dimensional dendritic crystals. Characteristic features of the perturbations appearing on the surface of a spherical body, leading to different scenarios of the…
The Mullineux map is a combinatorial function on partitions which describes the effect of tensoring a simple module for the symmetric group in characteristic $p$ with the one-dimensional sign representation. It can also be interpreted as an…
We revisit the R\'{e}dei-Berge symmetric function $\mathcal{U}_D$ for digraphs $D$, a specialization of Chow's path-cycle symmetric function. Through the lens of matrix algebra, we consolidate and expand on the work of Chow, Grinberg and…
Smooth parametrization consists in a subdivision of the mathematical objects under consideration into simple pieces, and then parametric representation of each piece, while keeping control of high order derivatives. The main goal of the…
The purpose of this article is to give an explicit description, in terms of hypergeometric functions over finite fields, of zeta function of a certain type of smooth hypersurfaces that generalizes Dwork family. The point here is that we…
We discuss the impact of different measurements of the dbar/ubar asymmetry in the extraction of parameterizations of parton distribution functions.
One definition of key polynomials is as the weight generating functions of key tableaux. Assaf and Schilling introduced a crystal structure on key tableaux and related it to Morse--Schilling crystals on reduced factorizations for…
We consider the symmetry property of the inelastic overlap function and its relation to the reflective scattering mode appearance.
Momentum-space nonsymmorphic symmetries have recently attracted significant interest in both artificial and condensed-matter crystals, whereas real-space nonsymmorphic symmetries have long played an important role in the study of…
The differential geometric aspects of Geometric Phases are reviewed.
We review some of the interplay between mirror symmetry and K3 surfaces.
Symmetries are so involved in crystallographic detail that it is indispensable when crystal cell or lattice is mentioned. For nanocrystals, however, many are 'systemic symmetries', meaning that the whole structures of nanocrystal particles…
We survey old and new conjectures and results on various types of spherical maximal functions, emphasizing problems with a fractal dilation set.
Unparticles are realized by deconstruction in higher extra dimensions. It is shown that in this framework when the scale invariance is broken, the corresponding spectral function of the unparticle is shifted by an amount of the breaking…
This paper makes precise the close connection between the affine Hecke algebra, the path model, and the theory of crystals. Section 2 is a basic pictorial exposition of Weyl groups and affine Weyl groups and Section 5 is an exposition of…
The classical theory of symmetric functions has a central position in algebraic combinatorics, bridging aspects of representation theory, combinatorics, and enumerative geometry. More recently, this theory has been fruitfully extended to…
Critical points of an invariant function may or may not be symmetric. We prove, however, that if a symmetric critical point exists, those adjacent to it are generically symmetry breaking. This mathematical mechanism is shown to carry…