Paths and tableaux descriptions of Jacobi-Trudi determinant associated with quantum affine algebra of type C_n

We study the Jacobi-Trudi-type determinant which is conjectured to be the q-character of a certain, in many cases irreducible, finite-dimensional representation of the quantum affine algebra of type C_n. Like the D_n case studied by the authors recently, applying the Gessel-Viennot path method with an additional involution and a deformation of paths, we obtain a positive sum expression over a set of tuples of paths, which is naturally translated into the one over a set of tableaux on a skew diagram.Comment: 21 pages, 10 figures, the final (journal) version published in SIGMA at http://www.emis.de/journals/SIGMA

ダニアレルギー性鼻炎における上皮系サイトカイン(IL-33,IL-25,TSLP)の役割

学位の種別: 課程博士審査委員会委員 : (主査)東京大学教授 長瀬 隆英, 東京大学准教授 岩崎 真一, 東京大学准教授 菅谷 誠, 東京大学特任准教授 新井 郷子, 東京大学講師 藤尾 圭志University of Tokyo(東京大学

Reassociation of annelid giant hemoglobin from the polychaete Perinereis aibuhitensis

Annelid extracellular hemoglobin (Hb) is a supramolecule with molecular mass of ～3,500kDa. The giant Hb consists of 12 subassemblies (globin dodecamers, D) and 18 homodimeric linkers (L) of non-globin chain. The globin dodecamer and linker were isolated from the polychaete Perinereis aibuhittensis Hb separately. Subsequently, these two components were mixed in the presence of 1M urea at a neutral pH to reform a whole molecule of Hb. At first L was refined by reverse phase chromatography in organic solvent. On the other hand, Perinereis Hb was incubated in 4M urea solution at 4°C for 5 min, and applied to two amphoteric ion-exchange resin column to remove L stick to the resin, and to isolate only D. The eluate was condensed and subjected to gel filtration. As a result, an ingredient of molecule mass ～210 kDa, that is D, was provided in high yield. When D and L were mixed in the molar ratio of approximately 1:1 in 50mM phosphate buffer (pH 7.2) in the presence of 1 M urea at room temperature, most of the proteins met to natural Hb size again within about 20 hours. Furthermore, similar experiments were performed in 50 mM Tris-HCl buffer (pH 7.2) containing 1 M urea in the presence of 1 mM CaCl2 or 1mM EDTA. It was observed that the reassociation was affected substantially by the presence of Ca2+. In conclusion, the homodimeric linkers have the key role to form the gigantic Hb

Symmetry, Integrability and Geometry: Methods and Applications Paths and Tableaux Descriptions of Jacobi–Trudi Determinant Associated with Quantum Affine Algebra of Type Cn

Abstract. We study the Jacobi–Trudi-type determinant which is conjectured to be the q-character of a certain, in many cases irreducible, finite-dimensional representation of the quantum affine algebra of type Cn. Like the Dn case studied by the authors recently, applying the Gessel–Viennot path method with an additional involution and a deformation of paths, we obtain an expression by a positive sum over a set of tuples of paths, which is naturally translated into the one over a set of tableaux on a skew diagram