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### A monoidal localization theorem for the small quantum group

**Algebra & Discrete Mathematics**

Speaker: | Cris Negron, University of South California |

Related Webpage: | https://dornsife.usc.edu/negron |

Location: | 1147 MSB |

Start time: | Mon, May 23 2022, 11:00AM |

I will talk about joint work with Julia Pevtsova (arXiv:2203.10764), which concerns the small quantum group $u_q(G)$. Here $G$ is a complex reductive group and q is a root of unity in

$\mathbb{C}$.We show that the category of representations for $u_q(G)$ admits a fully faithful tensor embedding into the category of coherent sheaves over a “quantum” flag variety. This quantum flag variety is, essentially, some exotic, finitely fibered space over the classical flag variety $G/B$.I will explain how this embedding theorem codifies relationships between the small quantum group and its quantum Borels, and discuss consequences in both support theory and geometric representation theory.