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arXiv · 2007.15573

Jacobi-Trudi identity and Drinfeld functor for super Yangian

Kang Lu·Evgeny Mukhin
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Abstract

We show that the quantum Berezinian which gives a generating function of the integrals of motions of XXX spin chains associated to super Yangian $\mathrm{Y}(\mathfrak{gl}_{m|n})$ can be written as a ratio of two difference operators of orders $m$ and $n$ whose coefficients are ratios of transfer matrices corresponding to explicit skew Young diagrams. In the process, we develop several missing parts of the representation theory of $\mathrm{Y}(\mathfrak{gl}_{m|n})$ such as $q$-character theory, Jacobi-Trudi identity, Drinfeld functor, extended T-systems, Harish-Chandra map.

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BibTeXRIS

Kang Lu, Evgeny Mukhin. 2020-07-30. Jacobi-Trudi identity and Drinfeld functor for super Yangian. https://doi.org/10.1093/imrn%2Frnab023

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