Theoretical analysis characterizes irreducible weight modules over map extended Special Lie algebras, identifying them as rescaled irreducible Jet modules.
We study a class of irreducible uniformly bounded weight modules for map extended Special Lie algebra [Formula: see text]([Formula: see text]), where the elements [Formula: see text] and [Formula: see text] act nontrivially on such modules for some nonzero [Formula: see text]. It is shown these modules are irreducible for the underlying extended Special algebra [Formula: see text] with finite-dimensional weight spaces, which are precisely the irreducible Jet modules(with some rescaled variable) for the Lie algebra [Formula: see text] with finite-dimensional weight spaces.
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Bisht et al. (2026) studied this question.
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