Unipotent Quantum Coordinate Ring and Prefundamental Representations for Types A(1)n and D(1)n

Il Seung Jang, Jae Hoon Kwon, Euiyong Park

Research output: Contribution to journalArticlepeer-review

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Abstract

We give a new realization of the prefundamental representations L±r,a introduced by Hernandez and Jimbo, when the quantum loop algebra Uq(g) is of types A(1)n and D(1)n and the r-th fundamental weight (Equation presented)r for types An and Dn is minuscule. We define an action of the Borel subalgebra Uq(b) of Uq(g) on the unipotent quantum coordinate ring associated to the translation by -(Equation presented)r and show that it is isomorphic to L±r,a. We then give a combinatorial realization of L+r,a in terms of the Lusztig data of the dual PBW vectors.

Original languageEnglish
Pages (from-to)1119-1172
Number of pages54
JournalInternational Mathematics Research Notices
Volume2023
Issue number2
DOIs
StatePublished - 1 Jan 2023

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