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- W3136806602 abstract "We study the category O of representations over a shifted Yangian. This category has a tensor product structure and contains distinguished modules, the positive prefundamental modules and the negative prefundamental modules. Motivated by the representation theory of the Borel subalgebra of a quantum affine algebra and by the relevance of quantum integrable systems in this context, we prove that tensor products of prefundamental modules with irreducible modules are either cyclic or co-cyclic. This implies the existence and uniqueness of morphisms, the R-matrices, for such tensor products. We prove the R-matrices are polynomial in the spectral parameter, and we establish functional relations for the R-matrices. As applications, we prove the Jordan--Holder property in the category O. We also obtain a proof, uniform for any finite type, that any irreducible module factorizes through a truncated shifted Yangian." @default.
- W3136806602 created "2021-03-29" @default.
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- W3136806602 date "2021-03-19" @default.
- W3136806602 modified "2023-09-26" @default.
- W3136806602 title "Shifted Yangians and polynomial R-matrices" @default.
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- W3136806602 doi "https://doi.org/10.48550/arxiv.2103.10993" @default.
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