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 rational nested Bethe ansatz (RNBA) equations are constructed using the ``completed Calogero-Moser phase space'' of matrices which satisfy a finite dimensional analogue of the canonical commutation relationship. A key feature is the fact that the RNBA equations are derived only from this commutation relationship and some elementary linear algebra. The solutions constructed in this way inherit continuous and discrete symmetries from the CM phase space.
- Pub Date:
- April 2000
- Mathematical Physics;
- Mathematics - Dynamical Systems;
- Mathematics - Mathematical Physics;
- Mathematics - Quantum Algebra;
- Mathematics - Rings and Algebras
- to appear in "Regular and Chaotic Dynamics"