Seminar| Institute of Mathematical Sciences
Time:Friday, May 16th, 2025,15:00-16:00
Abstract:Let U^- be the negative half of the quantum group of finite type.U^- has good bases, called canonical bases and PBW bases. Canonical bases are important for the representation theory of quantum groups. But the direct computation of canonical bases is difficult. Since the construction of PBW bases is more elementary, it is important to know the transition matrix P between canonical bases and PBW bases. In this talk, we show that there exists a simple algorithm of computing the matrix P.
By the folding theory of quantum groups, the quantum group U_1^- of symmetric type, with an automorphism, is closely related to the quantum group U_2^- of non-symmetric type, such as U_1^- of type A_{2n-1} and U_2^- of type B_n. We discuss about the comparison of algorithms for U_1^- and for U_2^-.