Algebra Seminar

After telling the successful story of crystal bases of Kac-Moody Lie algebras in "On crystal bases" (CMS Conference Proc. Vol. 16, AMS, 1995), Kashiwara asked the following question: Is there an analogue of the crystal base and global base for the q-analogues of other algebras? Finite dimensional simple Lie algebras are part of the finite dimensional simple Lie superalgebras, it is natural to seek an answer to this question for finite dimensional Lie superalgebras. This talk will survey some of the recent developments of crystal base theory for Lie superalgebras.