Abstract
We provide a new approach towards the analysis of the fusion products defined by B. Feigin and S. Loktev in the representation theory of (truncated) current Lie algebras. We understand the fusion product as a degeneration using Gröbner theory of non-commutative algebras and outline a strategy on how to prove a conjecture about the defining relations for the fusion product of two evaluation modules. We conclude with following this strategy for \(\mathfrak {sl}_2(\mathbb {C}[t]) \) and hence provide yet another proof for the conjecture in this case.
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Acknowledgements
J. Flake and V. Levandovskyy were partially funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) through Project-ID 286237555 of TRR 195.
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Presented by: Vyjayanthi Chari
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Flake, J., Fourier, G. & Levandovskyy, V. Gröbner Bases for Fusion Products. Algebr Represent Theor 26, 2235–2253 (2023). https://doi.org/10.1007/s10468-022-10179-6
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DOI: https://doi.org/10.1007/s10468-022-10179-6