Partial Differential system in two variables with $W(D_6^{(1)})$-symmetry and the Garnier system in two variables

Abstract

In this note, we will compare the Garnier system in two variables with four-dimensional partial differential system in two variables with $W(D_6^{(1)})$-symmetry. Both systems are different in each compactification in the variables $q_1,q_2$, however, has same five holomorphy conditions in the variables $p_1,p_2$.