代数与表示论专题报告——The Unicity Theorem and the center of the SL3-skein algebra

Speaker: Dr. Zhihao Wang (王志浩 博士)

  (新加坡Nanyang Technological Univ. and 荷兰Univ. of Groningen.)

Time: 3:00-5:00pm, Oct. 23 (Wednesday), 2024

Place: 浙江大学紫金港校区海纳苑二号楼101

Abstract:  

SL_n-skein algebra is related to character variety, Higher Teichmüller theory, and cluster algebra. For example, the reduced stated SL2-skein algebra has proved to be isomorphic to the quantum cluster algebra when the surface has no interior punctures.

I will review the definition of the SL₃-skein algebra of a surface, which is a quantum deformation of the coordinate algebra of the SL3-character variety of this surface.

I will talk about the Unicity Theorem of the SL₃-skein algebra, which classifies the irreducible representations of the SL₃-skein algebra. I will talk about the center and the PI-degree of the SL₃-skein algebra. The PI-degree of the  SL₃-skein algebra equals the maximal dimension of irreducible representations of the  SL₃-skein algebra.