Aspects of q-discretized Nahm equations

摘要

There is a conjecture by Ward that almost all of integrable equations are derived from (anti-)self-dual (ASD) Yang-Mills equations. This conjecture is supported by many concrete examples, e.g., the Nahm equations. In this work, we consider a situation that if the ASD conditions are slightly loosened, as to how it affects the integrability of the equations. For this purpose, we consider a q-analog of the Nahm equations, as a non-ASD system. The analysis is performed on the reduced system which is a q-analog of the Euler-Arnold top, by the singularity confinement test and the estimation of the algebraic entropy.