Quantum loop groups for symmetric Cartan matrices

2022/07/12 by Andrei Neguţ, Neguţ, Andrei · 1 citation
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2207.05504

openalex publication_date 2022/07/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 ∈ I, k ∈ 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 ℂ^* action.

Cited by

• Quiver moduli and quantum loop algebras

Related

• Quantum loop groups and K-theoretic stable envelopes
• Quantum loop groups for arbitrary quivers
• Hall algebras and quantum symmetric pairs of Kac-Moody type II
• Non symmetric quantum loop groups and K-theory
• \imathHall algebras and \imathquantum groups