# Exterior powers of the adjoint representation and the Weyl ring of $E_8$

@article{Brini2019ExteriorPO,
title={Exterior powers of the adjoint representation and the Weyl ring of \$E\_8\$},
author={A. Brini},
journal={arXiv: Representation Theory},
year={2019}
}
• A. Brini
• Published 2019
• Mathematics, Physics
• arXiv: Representation Theory
I derive explicitly all polynomial relations in the character ring of $E_8$ of the form $\chi_{\wedge^k \mathfrak{e}_8} - \mathfrak{p}_{k} (\chi_{1}, \dots, \chi_{8})=0$, where $\wedge^k \mathfrak{e}_8$ is an arbitrary exterior power of the adjoint representation and $\chi_{i}$ is the $i^{\rm th}$ fundamental character. This has simultaneous implications for the theory of relativistic integrable systems, Seiberg-Witten theory, quantum topology, orbifold Gromov-Witten theory, and the arithmetic… Expand
2 Citations

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