Quantization of symmetric spaces and canonical bases
数学专题报告
报告题目(Title)：Quantization of symmetric spaces and canonical bases
报告人(Speaker)：宋金峰（新加坡国立大学）
地点(Place)：后主楼1223
时间(Time)：12月11日下午16:00-17:00
邀请人(Inviter)：肖杰、覃帆、周宇、方杰鹏、兰亦心
报告摘要
Let G be a connected reductive group over an algebraically closed field. Let $\theta$ be a group involution and K be the fixed point subgroup. The affine quotient G/K is called a symmetric space. In this talk, I will describe a quantization of the algebra of regular functions on the symmetric space, together with a canonical basis on the quantized coordinate algebra. By the specialization, we get an integral model of the symmetric space and a good filtration on its coordinate algebra. Our construction makes essential use of the canonical bases arising from quantum symmetric pairs. The group G itself can be viewed as a symmetric space. In this case, our construction recovers Lusztig’s construction of the Chevalley group schemes via quantum groups. This is joint work with Huanchen Bao.
