i-quantum groups are certain coideal subalgebras of quantum groups appearing in the theory of quantum symmetric pairs. Many results concerning quantum groups have been generalized to i-quantum groups. However, representation theory of i-quantum groups is much more difficult than that of quantum groups due to the lack of Chevalley-like generators. In this talk, I introduce the notion of classical weight modules over i-quantum groups, and explain that they can be thought of as counterparts of the weight modules over quantum groups.

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