Finite-dimensional tau functions of the universal character hierarchy
Chuanzhong Li
Abstract
Using the so-called Schubert decomposition, we present a finite-dimensional twisted description of the tau functions of the universal character (UC ) hierarchy using Grassmannians. Moreover, from the standpoint of the relation between the UC and Kadomtsev–Petviashvili hierarchies, we study the expansion of this tau function in terms of the action of Abelian groups on finite-dimensional Grassmannians. We use the Gekhtman–Kasman determinant formula involving exponentials of finite-dimensional matrices, which naturally leads to the structure of two finite Grassmannians. Using the Gekhtman–Kasman-type formula, we consider some concrete examples: rational, soliton, and mixed solutions.
Topics & Concepts
Character (mathematics)MathematicsHierarchyPure mathematicsAction (physics)Abelian groupType (biology)Function (biology)Algebra over a fieldPhysicsGeometryQuantum mechanicsBiologyMarket economyEconomicsEvolutionary biologyEcologyMolecular spectroscopy and chiralityAdvanced Combinatorial MathematicsAlgebraic structures and combinatorial models