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arXiv · 1508.07057

Quantum groups, quantum tori, and the Grothendieck-Springer resolution

Gus Schrader·Alexander Shapiro
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Abstract

We construct an algebra embedding of the quantum group $U_q(\mathfrak{g})$ into the quantum coordinate ring $\mathcal{O}_q[G^{w_0,w_0}/H]$ of the reduced big double Bruhat cell in $G$. This embedding factors through the Heisenberg double $\mathcal{H}_q$ of the quantum Borel subalgebra $U_{\geq0}$, which we relate to $\mathcal{O}_q[G]$ via twisting by the longest element of the quantum Weyl group. Our construction is inspired by the Poisson geometry of the Grothendieck-Springer resolution studied by Evens and Lu, and the quantum Beilinson-Bernstein theorem investigated by Backelin, Kremnitzer, and Tanisaki.

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Gus Schrader, Alexander Shapiro. 2017-01-20. Quantum groups, quantum tori, and the Grothendieck-Springer resolution. https://arxiv.org/abs/1508.07057

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