English

Unipotent quantum coordinate ring and minuscule prefundamental representations: twisted case

Representation Theory 2025-12-08 v2 Quantum Algebra

Abstract

We study the prefundamental modules Ls,a±L_{s,a}^{\pm} over the Borel subalgebras of the twisted quantum loop algebras, which are introduced by Wang. A character formula for Ls,a±L_{s,a}^{\pm} is obtained from that for the prefundamental modules over the untwisted quantum loop algebras by applying a character folding map. This allows us to realize minuscule prefundamental modules Ls,a±L_{s,a}^{\pm} for types A2n1(2)A_{2n-1}^{(2)} and Dn+1(2)D_{n+1}^{(2)} in terms of the unipotent quantum coordinate ring associated with the ss-th level 00 fundamental weight, where s=1s = 1 for type A2n1(2)A_{2n-1}^{(2)} and s=ns = n for type Dn+1(2)D_{n+1}^{(2)}. This result is a continuation of the realization of (co)minuscule prefundamental modules established by earlier works [J-Kwon-Park, Int. Math. Res. Not., 2023] and [J-Kwon-Park, J. Algebra, 2025].

Keywords

Cite

@article{arxiv.2512.02946,
  title  = {Unipotent quantum coordinate ring and minuscule prefundamental representations: twisted case},
  author = {Il-Seung Jang},
  journal= {arXiv preprint arXiv:2512.02946},
  year   = {2025}
}

Comments

v2: 29 pages, revised proof of Theorem 6.7, minor corrections; v1: 28 pages

R2 v1 2026-07-01T08:06:00.752Z