Gröbner bases for fusion products

arXiv (Cornell University)

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.

Authors 3

1. Johannes Flake Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University , Pontdriesch 10-16 , 52062 Aachen

2. Ghislain Fourier Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University , Pontdriesch 10-16 , 52062 Aachen

3. Viktor Levandovskyy Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University , Pontdriesch 10-16 , 52062 Aachen