English

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

Representation Theory 2024-11-14 v3 Mathematical Physics math.MP Quantum Algebra

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 AA 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.

Keywords

Cite

@article{arxiv.2408.00615,
  title  = {Quantum difference equations and Maulik-Okounkov quantum affine algebras of affine type $A$},
  author = {Tianqing Zhu},
  journal= {arXiv preprint arXiv:2408.00615},
  year   = {2024}
}

Comments

58 pages. Some typo fixed. The proof of Proposition 4.2 refined. Reference added. Comments are welcome!