Irreducibility of Certain $\widehat{\mathfrak{sl}}_2$-Modules of Wakimoto Type
Quantum Algebra
2026-05-25 v2 Mathematical Physics
math.MP
Representation Theory
Abstract
We investigate the irreducible smooth -modules recently constructed in [Adv. Math. 481 (2025), 110559, 34 pages, arXiv:2404.03855], and demonstrate that these modules admit a Wakimoto-type realization at both critical and non-critical levels. In the critical level case, we identify simple quotients of these modules with the Wakimoto modules whose irreducibility was already established by Adamovi\'c. We also generalize some Wakimoto modules constructed in [Adv. Math. 289 (2016), 438-479, arXiv:1409.5354] and identify them as generalized Whittaker modules.
Keywords
Cite
@article{arxiv.2512.02718,
title = {Irreducibility of Certain $\widehat{\mathfrak{sl}}_2$-Modules of Wakimoto Type},
author = {Dražen Adamović and Veronika Pedić Tomić},
journal= {arXiv preprint arXiv:2512.02718},
year = {2026}
}