Abstract
We identify level one global Weyl modules for toroidal Lie algebras with certain twists of modules constructed by Moody–Eswara Rao–Yokonuma via vertex operators for type ADE and by Iohara–Saito–Wakimoto and Eswara Rao for general type. The twist is given by an action of \(\mathrm {SL}_{2}(\mathbb {Z})\) on the toroidal Lie algebra. As a by-product, we obtain a formula for the character of the level one local Weyl module over the toroidal Lie algebra and that for the graded character of the level one graded local Weyl module over an affine analog of the current Lie algebra.
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Acknowledgements
The author is grateful to Ryo Sato who pointed out that the result of [6] can be used to improve this work. He also would like to thank Yoshihisa Saito and Kentaro Wada for helpful discussion. This work was supported by JSPS KAKENHI Grant Numbers 17H06127 and 18K13390.
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Kodera, R. Level one Weyl modules for toroidal Lie algebras. Lett Math Phys 110, 3053–3080 (2020). https://doi.org/10.1007/s11005-020-01321-w
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DOI: https://doi.org/10.1007/s11005-020-01321-w