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We study irreducible modules for map Heisenberg–Virasoro algebras. In particular, we give a complete classification of irreducible Harish–Chandra modules for map Heisenberg–Virasoro algebras. We will also classify non-weight irreducible modules for map Heisenberg–Virasoro algebras whose restriction on the degree zero part of the universal enveloping algebra of Witt algebra is free of rank 1.
Priyanshu Chakraborty (Sun,) studied this question.