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arXiv · 2003.05639

Gröbner bases for fusion products

Johannes Flake·Ghislain Fourier·Viktor Levandovskyy
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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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Johannes Flake, Ghislain Fourier, Viktor Levandovskyy. 2021-01-07. Gröbner bases for fusion products. https://arxiv.org/abs/2003.05639

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