Gröbner Bases for Fusion Products

Abstract

AbstractWe 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]) $ s l 2 ( ℂ [ t ] ) and hence provide yet another proof for the conjecture in this case.