On the Cluster Nature and Quantization of Geometric -Matrices

  • Rei Inoue

    Chiba University, Japan
  • Thomas Lam

    University of Michigan, Ann Arbor, USA
  • Pavlo Pylyavskyy

    University of Minnesota, Minneapolis, USA
On the Cluster Nature and Quantization of Geometric $R$-Matrices cover

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Abstract

We define cluster -matrices as sequences of mutations in triangular grid quivers on a cylinder, and show that the affine geometric -matrix of symmetric power representations for the quantum affine algebra can be obtained from our cluster -matrix. A quantization of the affine geometric -matrix is defined, compatible with the cluster structure. We construct invariants of the quantum affine geometric -matrix as quantum loop symmetric functions.

Cite this article

Rei Inoue, Thomas Lam, Pavlo Pylyavskyy, On the Cluster Nature and Quantization of Geometric -Matrices. Publ. Res. Inst. Math. Sci. 55 (2019), no. 1, pp. 25–78

DOI 10.4171/PRIMS/55-1-2