research article
Quantum loop groups for symmetric Cartan matrices
February 5, 2026
We introduce a quantum loop group associated to a general symmetric Cartan matrix, by imposing just enough relations between the usual generators {e_{i,k},f_{i,k}}_{i\in I,,k\in\mathbb{Z}} in order for the natural Hopf pairing between the positive and negative halves of the quantum loop group to be perfect. As an application, we describe the localized 𝐾-theoretic Hall algebra of any quiver without loops, endowed with a particularly important \mathbb{C}^{*} action.
Type
research article
Author(s)
École Polytechnique Fédérale de Lausanne
Date Issued
2026-02-05
Publisher
Editorial or Peer reviewed
REVIEWED
Written at
EPFL
EPFL units
Available on Infoscience
February 17, 2026
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