Combinatorial realizations of crystals via torus actions on quiver varieties

Consider Kashiwara's crystal associated to a highest weight representation of a symmetric Kac-Moody algebra. There is a geometric realization of this object using Nakajima's quiver varieties, but in many particular cases it can also be realized by elementary combinatorial methods. Here we propose a framework for extracting combinatorial realizations from the geometric picture: We construct certain torus actions on the quiver varieties and use Morse theory to index the irreducible components by connected components of the subvariety of torus fixed points. We then discuss the case of affine sl(n). There the fixed point components are just points, and are naturally indexed by multi-partitions. There is some choice in our construction, leading to a family of combinatorial models for each highest weight crystal. Applying this construction to the crystal of the fundamental representation recovers a family of combinatorial realizations recently constructed by Fayers. This gives a more conceptual proof of Fayers' result as well as a generalization to higher level. We also discuss a relationship with Nakajima's monomial crystal.Comment: 23 pages, v2: added Section 8 on monomial crystals and some references; v3: many small correction

Weight Vectors of the Basic A_1^(1)-Module and the Littlewood-Richardson Rule

The basic representation of \A is studied. The weight vectors are represented in terms of Schur functions. A suitable base of any weight space is given. Littlewood-Richardson rule appears in the linear relations among weight vectors.Comment: February 1995, 7pages, Using AMS-Te

Non-universal Efimov Atom-Dimer Resonances in a Three-Component Mixture of 6Li

We observed an enhanced atom-dimer relaxation due to the existence of Efimov states in a three-component mixture of 6Li atoms. We measured the magnetic-field dependence of the atom-dimer loss coefficient in the mixture of atoms in state |1> and dimers formed in states |2> and |3>, and found two peaks corresponding to the degeneracy points of the |23> dimer energy level and energy levels of Efimov trimers. We found that the locations of these peaks disagree with universal theory predictions, in a way that cannot be explained by non-universal two-body properties. We constructed theoretical models that characterize the non-universal three-body physics of three-component 6Li atoms in the low energy domain.Comment: 5 pages, 3 figure

Cloud absorption properties as derived from airborne measurements of scattered radiation within clouds

Researchers briefly review the diffusion domain method for deriving the cloud similarity parameter and present preliminary analyses of the results thus far obtained. The presentation concentrates on the following points: (1) intercomparison of calibrated reflected intensities between the cloud absorption radiometer and the U.K. multispectral cloud radiometer; (2) quality control tests required to select those portions of an aircraft flight for which measurements are obtained within the diffusion domain; (3) case studies of the spectral similarity parameter of marine stratocumulus clouds; and comparisons of the experimentally-derived similarity parameter spectrum with that expected theoretically from the cloud droplet size distribution obtained from in situ observations

A-site Randomness Effect on Structural and Physical Properties of Ba-based Perovskite Manganites

The discovery of novel structural and physical properties in the $A$-site ordered manganite $R$BaMn$_{2}$O$_{6}$ ($R$ = Y and rare earth elements) has demanded new comprehension about perovskite manganese oxides. In the present study, the $A$-site disordered form, $R_{0.5}$Ba$_{0.5}$MnO$_{3}$, has been investigated and compared with both $R$BaMn$_{2}$O$_{6}$ and $R_{0.5}A_{0.5}$MnO$_{3}$ ($A$: Sr, Ca) in the structures and electromagnetic properties. $R_{0.5}$Ba$_{0.5}$MnO$_{3}$ has a primitive cubic perovskite cell in the structure and magnetic glassy states are dominant as its ground state, in contrast to the ordinary disordered $R_{0.5}A_{0.5}$MnO$_{3}$ ($A$: Sr, Ca). In Pr-compounds with various degrees of Pr/Ba randomness at the $A$-sites, the $A$-site disorder gradually suppresses both ferromagnetic and A-type antiferromagnetic transitions and finally leads to a magnetic glassy state in Pr$_{0.5}$Ba$_{0.5}$MnO$_{3}$. A peculiar behavior, multi-step magnetization and resistivity change, has been observed in Pr$_{0.5}$Ba$_{0.5}$MnO$_{3}$. These properties could be closely related to any spatial heterogeneity caused by the random distribution of Ba$^{2 +}$ and $R^{3 +}$ with much different ionic radius.Comment: 9 pages, to be published in J. Phys. Soc. Jpn. 73 Aug. (2004

On minimal affinizations of representations of quantum groups

In this paper we study minimal affinizations of representations of quantum groups (generalizations of Kirillov-Reshetikhin modules of quantum affine algebras introduced by Chari). We prove that all minimal affinizations in types A, B, G are special in the sense of monomials. Although this property is not satisfied in general, we also prove an analog property for a large class of minimal affinization in types C, D, F. As an application, the Frenkel-Mukhin algorithm works for these modules. For minimal affinizations of type A, B we prove the thin property (the l-weight spaces are of dimension 1) and a conjecture of Nakai-Nakanishi (already known for type A). The proof of the special property is extended uniformly for more general quantum affinizations of quantum Kac-Moody algebras.Comment: 38 pages; references and additional results added. Accepted for publication in Communications in Mathematical Physic

Langlands duality for finite-dimensional representations of quantum affine algebras

We describe a correspondence (or duality) between the q-characters of finite-dimensional representations of a quantum affine algebra and its Langlands dual in the spirit of q-alg/9708006 and 0809.4453. We prove this duality for the Kirillov-Reshetikhin modules and their irreducible tensor products. In the course of the proof we introduce and construct "interpolating (q,t)-characters" depending on two parameters which interpolate between the q-characters of a quantum affine algebra and its Langlands dual.Comment: 40 pages; several results and comments added. Accepted for publication in Letters in Mathematical Physic

Instantons on ALE spaces and Super Liouville Conformal Field Theories

We provide evidence that the conformal blocks of N=1 super Liouville conformal field theory are described in terms of the SU(2) Nekrasov partition function on the ALE space O_{P^1}(-2).Comment: 10 page

Footprints in the wind of Vela X-1 traced with MAXI

The stellar wind around the compact object in luminous wind-accreting high mass X-ray binaries is expected to be strongly ionized with the X-rays coming from the compact object. The stellar wind of hot stars is mostly driven by light absorption in lines of heavier elements, and X-ray photo-ionization significantly reduces the radiative force within the so-called Stroemgren region leading to wind stagnation around the compact object. In close binaries like Vela X-1 this effect might alter the wind structure throughout the system. Using the spectral data from Monitor of All-sky X-ray Image (MAXI), we study the observed dependence of the photoelectric absorption as function of orbital phase in Vela X-1, and find that it is inconsistent with expectations for a spherically-symmetric smooth wind. Taking into account previous investigations we develop a simple model for wind structure with a stream-like photoionization wake region of slower and denser wind trailing the neutron star responsible for the observed absorption curve.Comment: 5 pages, 3 figures, accepted in A&