For quantum loop algebras in type A, tensor products of two snake modules with a covering pair of ladders have explicitly described socles, and the first quotient in a natural submodule chain is simple and, under a mild condition, imaginary.
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Imaginary modules arising from tensor products of snake modules
For quantum loop algebras in type A, tensor products of two snake modules with a covering pair of ladders have explicitly described socles, and the first quotient in a natural submodule chain is simple and, under a mild condition, imaginary.