Loop realizations of quantum affine algebras
Sabin Cautis, Anthony Licata
TL;DR
This paper simplifies the loop presentation of quantum affine algebras, relates it to Drinfeld's realization, and introduces an idempotent version suitable for categorification, advancing understanding of their structure.
Contribution
It provides a simplified loop presentation of quantum affine algebras and defines an idempotent version for categorification purposes, connecting to Drinfeld's realization.
Findings
Simplified the description of quantum affine algebras in their loop form.
Connected the loop presentation to Drinfeld's realization via vertex operators.
Introduced an idempotent version suitable for categorification.
Abstract
We give a simplified description of quantum affine algebras in their loop presentation. This description is related to Drinfeld's new realization via halves of vertex operators. We also define an idempotent version of the quantum affine algebra which is suitable for categorification.
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