PIRSA:24050072

Quantum difference equations from shuffle algebra: affine type A quiver varieties

Zhu, T. (2024). Quantum difference equations from shuffle algebra: affine type A quiver varieties. Perimeter Institute. https://pirsa.org/24050072

Zhu, Tianqing. Quantum difference equations from shuffle algebra: affine type A quiver varieties. Perimeter Institute, May. 09, 2024, https://pirsa.org/24050072 

          @misc{ pirsa_PIRSA:24050072,
            doi = {10.48660/24050072},
            url = {https://pirsa.org/24050072},
            author = {Zhu, Tianqing},
            keywords = {Mathematical physics},
            language = {en},
            title = {Quantum difference equations from shuffle algebra: affine type A quiver varieties},
            publisher = {Perimeter Institute},
            year = {2024},
            month = {may},
            note = {PIRSA:24050072 see, \url{https://pirsa.org}}
          }

Tianqing Zhu

Tsinghua University

Talk number
PIRSA:24050072
Collection
Talk Type
Subject
Abstract

 

The quantum difference equation (qde) is the $q$-difference equation which is proposed by Okounkov and Smirnov to encode the $K$-theoretic twisted quasimap counting for the Nakajima quiver varieties. In this talk, we will give a direct quantum toroidal algebra $U_{q,t}(\hat{\hat{\mf{sl}}}_{n})$ construction for the qde of the affine type $A$ quiver varieties. We will show that there is a really explicit and concise formula for the quantum difference operators. Moreover we will show that the degeneration limit of the quantum difference equation is equivalent to the Dubrovin connection for the quantum cohomology of the affine type A quiver varieties, which will give the description of the monodromy representation of the Dubrovin connection via the monodromy operators in the quantum difference equation.

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