Geodesic
Relation between categories of representations of the~super-Yangian
Teoretičeskaâ i matematičeskaâ fizika, Tome 204 (2020) no. 3, pp. 466-484

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Using the approach developed by Toledano Laredo and Gautam, we introduce analogues of the category $\mathfrak{O}$ for representations of the Yangian $Y_\hbar(A(m,n))$ of a special linear Lie superalgebra and the quantum loop superalgebra $U_q(LA(m,n))$. We investigate the relation between them and conjecture that these categories are equivalent.
Keywords: Yangian of Lie superalgebra, quantum loop superalgebra, Yangian module, category $\mathfrak{O}$ of representations, Lie superalgebra, Drinfeld polynomial
Mots-clés : quantum $R$-matrix. 
@article{TMF_2020_204_3_a10,
     author = {V. A. Stukopin},
     title = {Relation between categories of representations of {the~super-Yangian}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {466--484},
     publisher = {mathdoc},
     volume = {204},
     number = {3},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2020_204_3_a10/}
}
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V. A. Stukopin. Relation between categories of representations of the~super-Yangian. Teoretičeskaâ i matematičeskaâ fizika, Tome 204 (2020) no. 3, pp. 466-484. http://geodesic.mathdoc.fr/item/TMF_2020_204_3_a10/