中科院数学与系统科学研究院
数学研究所
表示论研讨班
报告人：洪久族 教授（University of North Carolina at Chapel Hill）
题 目：Smooth locus of twisted affine Schubert varieties and twisted affine Demazure modules
时 间：2020.12.15（星期二），09:30-10:30
地 点：Zoom Meeting ID: 993 7155 2716 Passcode: 078934
摘 要：Zhu proved a duality theorem between level one affine Demazure modules and function rings of torus fixed point subschemes of affine Schubert varieties in affine Grassmannian. Using his methods and results, we prove a similar duality theorem between level one twisted affine Demazure modules and twisted affine Schubert varieties of absolutely special parahoric group scheme $\mathcal{G}$. As a consequence, we determine the smooth locus of all twisted affine Schubert varieties when$\mathcal{G}$ is of type A_{2n-1}^{(2)}, D_{n+1}^{(2)}, D_4^{(3)}. This confirm a conjecture of Haines and Richarz for these types. In fact, some partial results are also obtained for other types A_2n^{(2)}, E_6^{(2)}. We also give geometric descriptions of the Frenkel-Kac isomorphism for twisted affine Lie algebras, and the fusion product for twisted affine Demazure modules. This is a joint work with Marc Besson.
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