Abstract
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 (ŝln) 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) |
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Pages (from-to) | 25-78 |
Number of pages | 54 |
Journal | Publications of the Research Institute for Mathematical Sciences |
Volume | 55 |
Issue number | 1 |
DOIs | |
State | Published - 2019 |
Bibliographical note
Funding 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.
Publisher Copyright:
© 2019 Research Institute for Mathematical Sciences, Kyoto University.
Keywords
- Cluster algebra
- Geometric r-matrix
- Quantum cluster algebra