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arXiv · 2306.07947

An alternative proof of $\widehat{\mathfrak{sl}}_2'$ standard module semi-infinite structure

Timur Kenzhaev
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Abstract

B. Feigin and A. Stoyanovsky found the basis of semi-infinite monomials in standard $\widehat{\mathfrak{sl}}_2'$-module $L_{(0, 1)}$ with Lefschetz formula for the corresponding flag variety. These semi-infinite monomials are constructed by modes of the current $e(z) = \sum\limits_{n\in\mathbb{Z}} e_n\,z^{- n - 1}$. We give an alternative proof of this fact using explicit fermionic construction of this module. Namely, we realize $L_{(0, 1)}$ inside of the zero-charge subspace of Fermionic Fock space and show linear independence of vectors corresponding to semi-infinite monomials.

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BibTeXRIS

Timur Kenzhaev. 2023-06-11. An alternative proof of $\widehat{\mathfrak{sl}}_2'$ standard module semi-infinite structure. https://arxiv.org/abs/2306.07947

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