English

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 sl^2\widehat{\mathfrak{sl}}_{2}-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}
}