PreprintarXiv licencearXiv
Imaginary elements and crystals for quantum groups
Abstract
In this paper, we introduce the notion of stable imaginary elements in quantum groups and use crystal basis theory to construct explicit one-parameter families of such elements for all finite types. We show that all of Leclerc's examples of imaginary elements are stable imaginary. Using the generalized quantum Schur--Weyl duality, we also construct explicit examples of corresponding imaginary modules over quantum affine algebras of untwisted affine types.
Related
- Zeta elements for p-ordinary modular forms over imaginary quadratic fields and applications
- Bowen--Franks groups and minus class groups of imaginary abelian fields
- p-class groups in the cyclotomic ℤp-extension of imaginary quadratic fields
- Infinitely many finite simple groups of Lie type are not generated invariably by two elements of prime order
- Handlebodies separate elements of surface groups
BibTeX
@misc{lee2026imaginary,
title = {{Imaginary elements and crystals for quantum groups}},
author = {Kyu-Hwan Lee and Euiyong Park},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.32040},
eprint = {2610.32040},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.32040},
}
RIS
TY - UNPB
TI - Imaginary elements and crystals for quantum groups
AU - Kyu-Hwan Lee
AU - Euiyong Park
PY - 2026
DA - 2026/10/23
PB - arXiv
DO - 10.48550/arxiv.2610.32040
UR - https://arxiv.org/abs/2610.32040
AB - In this paper, we introduce the notion of stable imaginary elements in quantum groups and use crystal basis theory to construct explicit one-parameter families of such elements for all finite types. We show that all of Leclerc's examples of imaginary elements are stable imaginary. Using the generalized quantum Schur--Weyl duality, we also construct explicit examples of corresponding imaginary modules over quantum affine algebras of untwisted affine types.
ER -