Quantum difference equations and Maulik-Okounkov quantum affine algebras of affine type A

2024/08/01 by Tianqing Zhu, Zhu, Tianqing
Computer Science · Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Polynomial and algebraic computation #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2408.00615

openalex publication_date 2024/08/01 · openalex created_date 2024/08/04 · openalex updated_date 2026/07/28

Abstract

In this paper we prove the isomorphism of the positive half of the quantum toroidal algebra and the positive half of the Maulik-Okounkov quantum affine algebra of affine type A via the monodromy representation for the Dubrovin connection. The main tool is on the proof of the fact that the degeneration limit of the algebraic quantum difference equation is the same as that of the Okounkov-Smirnov geometric quantum difference equation.

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