An alternative proof of $\widehat{\mathfrak{sl}}_2'$ standard module semi-infinite structure
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866913264249602048 |
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| author | Kenzhaev, Timur |
| author_facet | Kenzhaev, Timur |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_07947 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | An alternative proof of $\widehat{\mathfrak{sl}}_2'$ standard module semi-infinite structure Kenzhaev, Timur Representation Theory Mathematical Physics 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. |
| title | An alternative proof of $\widehat{\mathfrak{sl}}_2'$ standard module semi-infinite structure |
| topic | Representation Theory Mathematical Physics |
| url | https://arxiv.org/abs/2306.07947 |