Quantum groups, quantum tori, and the Grothendieck–Springer resolution
Quantum groups, quantum tori, and the Grothendieck–Springer resolution
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量子群、量子环面和格洛腾迪克施普林格分辨率
DOI：
10.1016/j.aim.2017.09.010
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发表时间：
2017
影响因子：
1.7
通讯作者：
Shapiro, Alexander
中科院分区：
文献类型：
--
作者：
Schrader, Gus;Shapiro, Alexander
我们构造了量子群U q (g)的代数嵌入到g中简化的大双Bruhat元的量子坐标环O q [gw 0， w 0/H]的中心扩展中。这种嵌入因子通过量子Borel子代数U≥0的Heisenberg双H q来实现，我们通过量子Weyl群的最长元素扭转将其与O q [g]联系起来。我们的构建灵感来自于[10]中研究的Grothendieck-Springer分辨率的泊松几何，以及[2]和[36]中研究的量子贝林森-伯恩斯坦定理。
We construct an algebra embedding of the quantum group U q (g) into a central extension of the quantum coordinate ring O q [G w 0, w 0/H] of the reduced big double Bruhat cell in G. This embedding factors through the Heisenberg double H q of the quantum Borel subalgebra U≥ 0, which we relate to 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 in [10], and the quantum Beilinson–Bernstein theorem investigated in [2] and [36].