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Hirota equations associated with simply laced affine Lie algebras: The cuspidal class <i>E</i>6 of ${\mathfrak {e}}_6^{(1)}$e6(1)
In this paper we derive Hirota equations associated with the simply laced affine Lie algebras ${\mathfrak {g}}^{(1)}$g(1), where ${\mathfrak {g}}$g is one of the simply laced complex Lie algebras ${\mathfrak {a}}_n, {\mathfrak {d}}_n, {\mathfrak {e}}_6, {\mathfrak {e}}_7$an,dn,e6,e7 or ${\mathfrak {e}}_8$e8, defined by finite order automorphisms of ${\mathfrak {g}}$g which we …