Title:Computing the Haar state on the quantum group O(SL_q(3))
Speaker:Ting Lu（Texas A&M Univeristy）
Time:Wednesday, Dec27, 10:00-11:00
Location:Mingde Building, B201-1
Zoom Meeting，Meeting ID:958 1408 8126 , Password:128291
Abstract：The quantum group O(SL_q(3)) is an one-parameter deformation of the algebra of functions on the Lie group SL(n). The linear functional, Haar state, on O(SL_q(3)) is an analogue to the Haar measure on SL(n). The existence and uniqueness of the Haar state has been proven since 1969 by Seedler. However, computing the Haar state requires the knowledge of a special basis called Matrix Coefficients whose explicit exprressions are unknown when n>2. To find an efficient method to evaluate the Haar state, we define a special kind of monomials and prove that to compute the Haar state on O(SL_q(n)) it suffices to compute the Haar states of these special monomials. Finally, we provide an efficient method to compute the Haar state of the special monomials on O(SL_q(3)).
