10 papers
On the Quantization of a Self-Dual Integrable System
Alex Kasman
In this note, we apply canonical quantization to the self-dual particle system describing the motion of poles to a higher rank solution of the KP hierarchy, explicitly determining…
Integrable Systems and Rank One Conditions for Rectangular Matrices
Michael Gekhtman, Alex Kasman
We provide a determinantal formula for tau-functions of the KP hierarchy in terms of rectangular, constant matrices , and satisfying a rank one condition. This result is…
Nested Bethe Ansatz and Finite Dimensional Canonical Commutation Relations
Alex Kasman
Recent interest in discrete, classical integrable systems has focused on their connection to quantum integrable systems via the Bethe equations. In this note, solutions to the rati…
Commutative Partial Differential Operators
Alex Kasman, Emma Previato
In one variable, there exists a satisfactory classification of commutative rings of differential operators. In several variables, even the simplest generalizations seem to be unkno…
n-Schur Functions and Determinants on an Infinite Grassmannian
Alex Kasman
A set of functions is defined which is indexed by a positive integer and partitions of integers. The case reproduces the standard Schur polynomials. These functions are s…
Grassmannians, Nonlinear Wave Equations and Generalized Schur Functions
Alex Kasman
A set of functions is introduced which generalizes the famous Schur polynomials and their connection to Grasmannian manifolds. These functions are shown to provide a new method of…