We define cluster R-matrices as sequences of mutations in triangular grid quivers on a cylinder, and show that the affine geometric R-matrix of symmetric power representations for the quantum affine algebra U’ q (ŝl n ) can be obtained from our cluster R-matrix. A quantization of the affine geometric R-matrix is defined, compatible with the cluster structure. We construct invariants of the quantum affine geometric R-matrix as quantum loop symmetric functions.
|Original language||English (US)|
|Number of pages||54|
|Journal||Publications of the Research Institute for Mathematical Sciences|
|State||Published - 2019|
Bibliographical noteFunding Information:
We thank the anonymous referees for helpful comments. R.I. was partially supported by JSPS KAKENHI grants 26400037 and 16H03927. T.L. was partially supported by NSF grants DMS-1160726, DMS-1464693, and a Simons Fellowship. P.P. was partially supported by NSF grants DMS-1148634, DMS-1351590, and a Sloan Fellowship.
- Cluster algebra
- Geometric r-matrix
- Quantum cluster algebra