A classification of irreducible Wakimoto modules for the affine Lie algebra $A_1 ^{(1)}$

Drazen Adamovic

arxiv: 1402.6100 · v1 · pith:PJ3ZJQD7new · submitted 2014-02-25 · 🧮 math.QA · math.RT

A classification of irreducible Wakimoto modules for the affine Lie algebra A₁ ⁽¹⁾

Drazen Adamovic This is my paper

classification 🧮 math.QA math.RT

keywords wakimotoclassificationirreduciblemodulesaffinealgebraarxivcertain

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By using methods developed in arXiv:math/0602181 we study the irreducibility of certain Wakimoto modules for $\widehat{sl_2}$ at the critical level. We classify all $\chi \in {\Bbb C}((z))$ such that the corresponding Wakimoto module $W_{\chi}$ is irreducible. It turns out that zeros of Schur polynomials play important rule in the classification result.

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Irreducibility of Certain $\widehat{\mathfrak{sl}}_2$-Modules of Wakimoto Type
math.QA 2025-12 unverdicted novelty 4.0

Certain hat{sl}_2-modules admit Wakimoto realizations at critical and non-critical levels; simple quotients at critical level match known irreducible Wakimoto modules, and some Wakimoto modules are generalized as Whit...