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- W4387561376 abstract "We construct an element, which we call the Kirillov projector, that connects the topics of the title: on the one hand, it is defined using the Yangian of $mathfrak{gl}_N$, on the other hand, it gives a canonical projection onto the space of Whittaker vectors for any Whittaker module over the mirabolic subalgebra. Using the Kirillov projector, we deduce some categorical properties of Whittaker modules, for instance, we prove a mirabolic analog of Skryabin's theorem. We also show that it quantizes a rational version of the Cremmer-Gervais $r$-matrix. As application, we construct a universal vertex-IRF transformation from the standard dynamical $R$-matrix to this constant one in categorical terms." @default.
- W4387561376 created "2023-10-12" @default.
- W4387561376 creator A5027255206 @default.
- W4387561376 date "2023-10-10" @default.
- W4387561376 modified "2023-10-13" @default.
- W4387561376 title "Yangians, mirabolic subalgebras, and Whittaker vectors" @default.
- W4387561376 doi "https://doi.org/10.48550/arxiv.2310.06669" @default.
- W4387561376 hasPublicationYear "2023" @default.
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