Abstract:We investigate the irreducible smooth $\widehat{\mathfrak{sl}}_{2}$-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 Adamović. We also generalize some Wakimoto modules constructed in [Adv. Math. 289 (2016), 438-479, arXiv:1409.5354] and identify them as generalized Whittaker modules.
| Subjects: | Quantum Algebra (math.QA); Mathematical Physics (math-ph); Representation Theory (math.RT) |
| Cite as: | arXiv:2512.02718 [math.QA] |
| (or arXiv:2512.02718v2 [math.QA] for this version) | |
| https://doi.org/10.48550/arXiv.2512.02718 arXiv-issued DOI via DataCite |
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| Journal reference: | SIGMA 22 (2026), 052, 16 pages |
| Related DOI: | https://doi.org/10.3842/SIGMA.2026.052
DOI(s) linking to related resources |
From: Veronika Pedić Tomić [view email] [via Journal Sigma as proxy]
[v1]
Tue, 2 Dec 2025 12:51:23 UTC (16 KB)
[v2]
Thu, 21 May 2026 18:14:38 UTC (19 KB)
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