講演者： J. J. C. Nimmo 氏（Department of Mathematics, Glasgow University, UK）
日時： ２月　２４日（金）　　午後４時３０分から
場所： 青山学院大学　理工学部（相模原キャンパス）Ｌ棟６階　Ｌ６０３室

題目： 「On a nonabelian generalisation of the Hirota-Miwa equation」

要旨：
Perhaps the most well known three dimensional, fully discrete  
integrable system is the Hirota-Miwa or discrete KP equation. This  
talk will begin with a review some properties of this system paying  
particular attention to the construction of a family of exact  
solutions in the form of casoratian determinants by means of Darboux  
transformations. There are a number of features of the Hirota-Miwa  
equation that are essential for the construction but others aspects  
are inessential. By relaxing the inessential ones as much as possible  
while keeping the essential ones, we will obtain a integrable  
generalisation of the system with solutions in an associative algebra A, 
which is in general nonabelian. It will be seen that the action of Darboux 
transformations for the generalised system is very natural, corresponding 
merely to movement on a higher dimensional lattice. In the most abstract 
form the solutions obtained  by Darboux transformations are expressed as 
entries in the inverse of a matrix over A. When we take A to be a matrix  
algebra these expression lead to more familiar expressions for the  
solutions as ratios of multicomponents casoratian determinants.

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共催：　青山学院大学　理工学会