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• W3205161626 abstract "Abstract We give a new realization of the prefundamental representations $L^pm _{r,a}$ introduced by Hernandez and Jimbo, when the quantum loop algebra $U_q(mathfrak {g})$ is of types $A_n^{(1)}$ and $D_n^{(1)}$ and the $r$-th fundamental weight $varpi _r$ for types $A_n$ and $D_n$ is minuscule. We define an action of the Borel subalgebra $U_q(mathfrak {b})$ of $U_q(mathfrak {g})$ on the unipotent quantum coordinate ring associated to the translation by $-varpi _r$ and show that it is isomorphic to $L^pm _{r,a}$. We then give a combinatorial realization of $L^+_{r,a}$ in terms of the Lusztig data of the dual PBW vectors." @default.
• W3205161626 created "2021-10-25" @default.
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• W3205161626 date "2021-10-08" @default.
• W3205161626 modified "2023-10-14" @default.
• W3205161626 title "Unipotent Quantum Coordinate Ring and Prefundamental Representations for Types <i>A</i>n(1) and <i>D</i>n(1)" @default.
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• W3205161626 doi "https://doi.org/10.1093/imrn/rnab283" @default.
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