REPRESENTATION THEORY AND RELATED TOPICS SEMINAR

ABSTRACT: The Kazhdan-Lusztig theory offered a powerful solution to the difficult problem of determining the irreducible characters in the category O of a simple Lie algebra. In type A, the Kazhdan-Lusztig theory can be reformulated in terms of Lusztig's canonical bases of quantum groups via the quantized Schur duality. In this talk, we will discuss a new theory of canonical bases arising from quantum symmetric pairs, initiated in joint work with Weiqiang Wang, which allows a new formulation of the Kazhdan-Lusztig theory in type B via a generalized Schur duality. We use such new canonical bases to formulate and establish the Kazhdan-Lusztig theory for the category O of the ortho-symplectic Lie superalgebras for the first time.