Abstract
In this paper, we study the complex symmetry of Toeplitz operators on the weighted Bergman spaces over the unit polydisk. First, we completely characterize when anti-linear weighted composition operators [Formula: see text] are conjugations. We then give a sufficient and necessary condition for Toeplitz operators to be complex symmetric with respect to these conjugations. As a consequence, some interesting higher-dimensional complex symmetric phenomena appear on the unit polydisk such as the monomial Toeplitz operators [Formula: see text] with [Formula: see text] for some symmetric permutation matrix [Formula: see text]. Surprisingly, these operators [Formula: see text] are the only ones that are complex symmetric monomial Toeplitz operators on the unit bidisk.
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