Related papers: Polytopes for Crystallized Demazure Modules and Ex…
We study certain faces of the normal polytope introduced by Feigin, Littelmann and the author whose lattice points parametrize a monomial basis of the PBW-degenerated of simple modules for $\mathfrak{sl}_{n+1}$. We show that lattice points…
We discuss some extremal bases for $\CC$-convex domains.
In this paper, we give a new realization of crystal bases for finite dimensional irreducible modules over classical Lie algebras. The basis vectors are parameterized by certain Young walls lying between highest weight and lowest weight…
A complete classification of unimodular valuations on the set of lattice polygons with values in the spaces of polynomials and formal power series, respectively, is established. The valuations are classified in terms of their behaviour with…
In this paper we introduce and study the concept of set extremality for systems of convex sets in vector spaces without topological structures. Characterizations of the extremal systems of sets are obtained in the form of the convex…
We introduce a concept of multiplicity lattices of 2-multiarrangements, determine the combinatorics and geometry of that lattice, and give a criterion and method to construct a basis for derivation modules effectively.
Transportation matrices are $m\times n$ non-negative matrices whose row sums and row columns are equal to, or dominated above with given integral vectors $R$ and $C$. Those matrices belong to a convex polytope whose extreme points have been…
We study the extreme points of the cone of quasiconvex quadratic forms with linear elastic orthotropic symmetry. We prove that if the determinant of the acoustic matrix of the associated forth order tensor of the quadratic form is an…
We study symmetries of bases and spanning sets in finite element exterior calculus, using representation theory. We want to know which vector-valued finite element spaces have bases invariant under permutation of vertex indices. The…
There are two combinatorial ways of parameterizing the $J_b$-orbits of the irreducible components of affine Deligne-Lusztig varieties for $GL_n$ and superbasic $b$. One way is to use the extended semi-modules introduced by Viehmann. The…
We study pairs of finitely generated modules over a principal ideal domain and their corresponding matrix representations. We introduce equivalence relations for such pairs and determine invariants and canonical forms.
We give a criterion for the Demazure crystal $B_w(\lambda)$ defined by Kashiwara to have a tensor product structure. We study the $\sln$ symmetric tensor case, and see some Demazure characters are expressed using Kostka-Foulkes polynomials.
The evolution of a modulated positron beam in a planar crystal channel is investigated within the diffusion approach. A detailed description of the formalism is given. A new parameter, the demodulation length, is introduced, representing…
Let $\mathfrak{g}$ be a hyperbolic Kac-Moody algebra of rank $2$. We give a polyhedral realization of the crystal basis for the extremal weight module of extremal weight $\lambda$, where $\lambda$ is an integral weight whose Weyl group…
A lattice path matroid is a transversal matroid corresponding to a pair of lattice paths on the plane. A matroid base polytope is the polytope whose vertices are the incidence vectors of the bases of the given matroid. In this paper, we…
We present a simple and general method for construction of localized orbitals to describe electronic structure of extended periodic metals and insulators as well as confined systems. Spatial decay of these orbitals is found to exhibit…
The Mueller Matrix Polar Decomposition method decomposes a Mueller matrix into a diattenuator, a retarder, and a depolarizer. Among these elements, the retarder, which plays a key role in medical and material characterization, is modelled…
The concept of representing a polytope that is associated with some combinatorial optimization problem as a linear projection of a higher-dimensional polyhedron has recently received increasing attention. In this paper (written for the…
The goal of this paper is to study convex lattice sets by the discrete Legendre transform. The definition of the polar of convex lattice sets in $\mathbb{Z}^n$ is provided. It is worth mentioning that the polar of convex lattice sets have…
Given a finite set of vectors spanning a lattice and lying in a halfspace of a real vector space, to each vector $a$ in this vector space one can associate a polytope consisting of nonnegative linear combinations of the vectors in the set…