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arXiv · 1609.02483

Quantum exceptional group $G_2$ and its conjugacy classes

Alexander Baranov·Andrey Mudrov·Vadim Ostapenko
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Abstract

We construct quantization of semisimple conjugacy classes of the exceptional group $G=G_2$ along with and by means of their exact representations in highest weight modules of the quantum group $U_q(\mathfrak{g})$. With every point $t$ of a fixed maximal torus we associate a highest weight module $M_t$ over $U_q(\mathfrak{g})$ and realize the quantized polynomial algebra of the class of $t$ by linear operators on $M_t$. Quantizations corresponding to points of the same orbit of the Weyl group are isomorphic.

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Alexander Baranov, Andrey Mudrov, Vadim Ostapenko. 2016-09-08. Quantum exceptional group $G_2$ and its conjugacy classes. https://arxiv.org/abs/1609.02483

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