Abstract
We construct new families of \(U_q(\mathfrak {gl}_n)\)-modules by continuation from finite dimensional representations. Each such module is associated with a combinatorial object—admissible set of relations. More precisely, we prove that any admissible set of relations leads to a family of irreducible \(U_q(\mathfrak {gl}_n)\)-modules. Finite dimensional and generic modules are particular cases of this construction.
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Acknowledgements
V.F. is supported in part by CNPq (304467/2017-0) and by Fapesp (2014/09310-5). L.E.R. is supported by Fapesp (2018/17955-7) and J. Z. is supported by Fapesp (2015/05927-0).
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Dedicated to the 70th birthday of Ivan Shestakov.
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Futorny, V., Ramirez, L.E. & Zhang, J. Explicit construction of irreducible modules for \(U_q(\mathfrak {gl}_n)\). São Paulo J. Math. Sci. 13, 83–95 (2019). https://doi.org/10.1007/s40863-019-00123-w
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DOI: https://doi.org/10.1007/s40863-019-00123-w