A New Approach to Kazhdan-Lusztig Theory of Type B Via Quantum Symmetric Pairs

Download or read book A New Approach to Kazhdan-Lusztig Theory of Type B Via Quantum Symmetric Pairs written by Huanchen Bao and published by . This book was released on 2018 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: We show that Hecke algebra of type B and a coideal subalgebra of the type A quantum group satsify a double centralizer property, generalizing the Schur-Jimbo duality in type A. The quantum group of type A and its coideal subalgebra form a quantum symmetric pair. A new theory of canonical bases arising from quantum symmetric pairs is initiated. It is then applied to formulate and establish for the first time a Kazhdan-Lusztig theory for the BGG category [O] of the orthosymplectic Lie superalgebras osp(2m + 1[vertical bar]2n). In particular, our approach provides a new formulation of the Kazhdan-Lusztig theory for Lie algebras of type B/C.