相关论文: Realizations of Crystals
We discuss Nakamaye's Theorem and its recent extension to compact complex manifolds, together with some applications.
In this paper we primarily study monomial ideals and their minimal free resolutions by studying their associated LCM lattices. In particular, we formally define the notion of coordinatizing a finite atomic lattice P to produce a monomial…
Rewriting methods have been developed for the study of coherence for algebraic objects. This consists in starting with a convergent presentation, and expliciting a family of generating confluences to obtain a coherent presentation -- one…
Many crystals in nature exhibit fascinating mechanical, optical, magnetic and other characteristics. One of the reasons for this phenomenon has to do with the presence of specific organic molecules that are tightly associated with the…
We give a realization of crystal graphs for basic representations of the quantum affine algebra U_q(C_n^{(1)}) using combinatorics of Young walls. The notion of splitting blocks plays a crucial role in the construction of crystal graphs.
We describe points on Nakajima varieties and Weyl group actions on them via complexes of semisimple and projective modules over certain finite-dimensional algebras.
A widely spread method of crystal preparation is to precipitate it from a supersaturated solution. In such a process, control of solution concentration is of paramount importance. Nucleation process, polymorph selection, and crystal habits…
The magnitude for algebras is a generalization of the Euler characteristic. We investigate the magnitude for Nakayama algebras. Using Ringel's resolution quiver, the existence and the value of rational magnitude is given. As a result, we…
We discuss various aspects of representation of a polynomial as a sum of monomials (for example, uniqueness of such representation and related estimations).
For nonexceptional types, we prove a conjecture of Hatayama et al. about the prefectness of Kirillov-Reshetikhin crystals.
This paper gives a description of various recent results which construct monomial ideals with a given minimal free resolution. We show that these are all instances of coordinatizing a finite atomic lattice as defined by Mapes. Subsequently,…
When a light beam passes through a cascade of biaxial crystals with aligned optic axes, the resulting transverse intensity pattern consists of multiple concentric rings. We provide a simple formulation for the pattern formation for both…
We consider realization and isomorphism problems for formal matrix rings over a given ring. Principal multiplier matrices of such rings play an important role in this case.\\ The work of A.A.Tuganbaev is supported by Russian Scientific…
Single crystal growth is a widely explored method of synthesizing materials in the solid state. The last few decades have seen significant improvements in the techniques used to synthesize single crystals, but there has been comparatively…
We introduce a computational method to optimize target physical properties in the full configuration space regarding atomic composition, chemical stoichiometry, and crystal structure. The approach combines the universal potential of the…
In this survey we consider numerous known and unknown combinatorial realizations of the sequence A079487 and basic facts about it.
Let $B(\Lambda_0)$ be the level 1 highest weight crystal of the quantum affine algebra $U_q(A_n^{(1)})$. We construct an explicit crystal isomorphism between the geometric realization $\mathbb{B}(\Lambda_0)$ of $B(\Lambda_0)$ via quiver…
We shall describe the one-to-one correspondence between the set of pictures and the set of Littlewood-Richardson crystals.
We consider the Harmonic crystal, a measure on $\mathbb{R}^{\mathbb{Z}^{d}}$ with Hamiltonian $H(\x)=\sum_{i,j}J_{i,j}(\x(i)-\x(j))^{2}+ h\sum_{i}(\x(i)-\dd(i))^{2}$, where $\x, \dd$ are configurations, $\x(i),\dd(i)\in\mathbb{R}$,…
By using the Kang-Kashiwara-Misra-Miwa-Nakashima-Nakayashiki crystal base character formula for the basic $A_2^{(1)}$-module, and the principally specialized Weyl-Kac character formula, we obtain a Rogers-Ramanujan type combinatorial…