One fo the distinguished features of infinite dimensional Lie algebrs is the modular invariance of the characters of centain representations. There are two celebrated examples for this phenomena: One is the integrable highest weight reprfesentations of an affine Lie algebra g associated with a simplex Lie algebra a at a fixed level [KP], and the other is the minimal series representations [FFu] of the Virasoro algebra Vir with a fixed central charge.
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