Ind-Cluster Algebras & the Sato-Segal-Wilson Grassmannian

Christian Korff (University of Glasgow)

Tuesday 11th February 16:00-17:00 Maths 311B

Abstract

There is a bijection between solutions of the Kadomtsev-Petiashvili (KP) hierarchy and points on an infinite Grassmannian, now often simply referred to as "the Sato Grassmannian". This connection is made via the Pl"ucker coordinates, the expansion coefficients of the KP tau-function in the basis of Schur functions. That is, the KP tau-functions satisfy the Pl"ucker relations of all finite Grassmannians and their union forms what is known as the KP hierarchy. In other words, one considers the inductive limit of the coordinate rings of finite Grassmannians. A celebrated result is that the coordinate rings of finite Grassmannians carry a cluster algebra structure. We show that this cluster algebra structure can be extended to the inductive limit by introducing ind-cluster algebras. 

 

This is ongoing joint work with Sira Gratz, Aarhus Universitet.

 

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