# Cluster Realization of Positive Representations of a Split Real Quantum Borel Subalgebra

@article{Ip2017ClusterRO, title={Cluster Realization of Positive Representations of a Split Real Quantum Borel Subalgebra}, author={Ivan C. H. Ip}, journal={Theoretical and Mathematical Physics}, year={2017}, volume={198}, pages={215-238} }

Abstractour previous work, we studied positive representations of split real quantum groups $$\mathcal{U}_{q\widetilde{q}}(\mathfrak{g}_\mathbb{R})$$Uqq~(gR) restricted to their Borel part and showed that they are closed under taking tensor products. But the tensor product decomposition was only constructed abstractly using the GNS representation of a C*-algebraic version of the Drinfeld–Jimbo quantum groups. Here, using the recently discovered cluster realization of quantum groups, we write…

## 2 Citations

### Cluster realization of $$\mathcal {U}_q(\mathfrak {g})$$Uq(g) and factorizations of the universal R-matrix

- MathematicsSelecta Mathematica
- 2018

For each simple Lie algebra $$\mathfrak {g}$$g, we construct an algebra embedding of the quantum group $$\mathcal {U}_q(\mathfrak {g})$$Uq(g) into certain quantum torus algebra $$\mathcal…

### Cluster realization of Uq(g)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {U}_q(\mathfrak {g})$$\end{docume

- Materials ScienceSelecta Mathematica
- 2018

For each simple Lie algebra g\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs}…

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