Abstract
In this paper, we construct a series of additional flows of the C type Kadomtsev-Petviashvili (CKP) hierarchy and the multi-component CKP hierarchy, and these flows constitute an N-fold direct product of the positive half of the quantum torus symmetry. Comparing to the W∞ infinite dimensional Lie symmetry, this quantum torus symmetry has a nice algebraic structure with double indices.
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