Fusion Rules for Quantum Transfer Matrices as a Dynamical System on Grassmann Manifolds
Abstract
We show that the set of transfer matrices of an arbitrary fusion type for an integrable quantum model obeys these bilinear functional relations, which are identified with an integrable dynamical system on a Grassmann manifold (higher Hirota equation). The bilinear relations were previously known for a particular class of transfer matrices corresponding to rectangular Young diagrams. We extend this result for general Young diagrams. A general solution of the bilinear equations is presented.
 Publication:

Modern Physics Letters A
 Pub Date:
 1997
 DOI:
 10.1142/S0217732397001394
 arXiv:
 arXiv:solvint/9704015
 Bibcode:
 1997MPLA...12.1369L
 Keywords:

 Nonlinear Sciences  Exactly Solvable and Integrable Systems;
 High Energy Physics  Theory;
 Mathematics  Quantum Algebra
 EPrint:
 LaTex (MPLA macros included) 10 pages, 1 figure, included in the text