Related papers: A rigged configuration model for $B(\infty)$
Let $B(\Lambda)$ be a level $\ell$ highest weight crystal of the quantum affine algebra $U_q(A_n^{(1)})$. We construct an explicit crystal isomorphism between the geometric realization $\gB(\Lambda)$ of the crystal $B(\Lambda)$ using quiver…
We explicitly describe the isomorphism between two combinatorial realizations of Kashiwara's infinity crystal in types B and C. The first realization is in terms of marginally large tableaux and the other is in terms of Kostant partitions…
A model of diluted random field sustained by quenched volume deformations is shown to reproduce puzzling physical features found in X(CN)_{x}Y_{1-x} mixed cyanide crystals. X is an alkali metal (K, Na or Rb) and Y is a spherical halogen ion…
The B\"acklund problem is solved for both the compact and noncompact versions of the Ishimori (2+1)-dimensional nonlinear spin model. In particular, a realization of the arising B\"acklund algebra in the form of an infinite-dimensional loop…
Let $\mathfrak{g}$ be a hyperbolic Kac-Moody algebra of rank 2, and set $\lambda=\Lambda_{1} - \Lambda_{2}$, where $\Lambda_{1}$, $\Lambda_{2}$ are the fundamental weights. Denote by $V(\lambda)$ the extremal weight module of extremal…
We define three combinatorial models for \hat{sl(n)} crystals, parametrized by partitions, configurations of beads on an `abacus', and cylindric plane partitions, respectively. These are reducible, but we can identify an irreducible…
Kac-Moody groups over finite fields are finitely generated groups. Most of them can naturally be viewed as irreducible lattices in products of two closed automorphism groups of non-positively curved twinned buildings: those are the most…
The purpose of the study is to further investigate the classical Gibbs analysis of the heterogeneous system "stressed crystal - melt." It is demonstrated that each equilibrium configuration is stable with respect to a special class of…
The phase behavior of a single type of colloid C suspended in near-critical solvents is known to be very rich. Motivated in part by recent experiments we consider a mixture of two colloidal types C1 and C2 in a binary solvent close to its…
We give a brief overview and progress report on our lattice QCD calculation of neutral B mixing hadronic matrix elements needed for Standard Model and Beyond the Standard Model physics. Reference [1] contains more details and results.
A bijection is defined from Littlewood-Richardson tableaux to rigged configurations. It is shown that this map preserves the appropriate statistics, thereby proving a quasi-particle expression for the generalized Kostka polynomials, which…
Using Lakshmibai-Seshadri paths, we give a combinatorial realization of the crystal basis of an extremal weight module of integral extremal weight over the quantized universal enveloping algebra associated to the infinite rank affine Lie…
We review reformulation of the map from tensor product of crystals to the rigged configurations in terms of the energy function of affine crystals. Especially, we give intuitive picture of the inverse scattering formalism for the periodic…
We present a theoretical study of classical Wigner crystals in two- and three-dimensional isotropic parabolic traps aiming at understanding and quantifying the configurational uncertainty due to the presence of multiple stable…
We relate the combinatorial definitions of the type $A_n$ and type $C_n$ Stanley symmetric functions, via a combinatorially defined "double Stanley symmetric function," which gives the type $A$ case at $(\mathbf{x},\mathbf{0})$ and gives…
This paper establishes combinatorial characterisations of forced-symmetric and forced-periodic rigidity (under a fixed lattice) of bar-joint frameworks in non-Euclidean normed planes. In $\ell_q$-planes for $q\in(1,\infty)\backslash\{2\}$,…
In the preceding paper, we formulated a conjecture on the relations between certain classes of irreducible representations of affine Hecke algebras of type B and symmetric crystals for $\gl_\infty$. In the present paper, we prove the…
The set of finite binary matrices of a given size is known to carry a finite type A bicrystal structure. We first review this classical construction, explain how it yields a short proof of the equality between Kostka polynomials and…
In this note we describe a general elementary procedure to attach a fusion ring to any Kac-Moody algebra of affine type. In the case of untwisted affine algebras, they are usual fusion rings in the literature. In the case of twisted affine…
Necessary and sufficient conditions are obtained for the infinitesimal rigidity of braced grids in the plane with respect to non-Euclidean norms. Component rectangles of the grid may carry 0, 1 or 2 diagonal braces, and the combinatorial…