Super duality and irreducible characters of ortho-symplectic Lie superalgebras

Shun-Jen Cheng, Ngau Lam, Weiqiang Wang

Published 2009-11-01, updated 2010-08-10Version 2

We formulate and establish a super duality which connects parabolic categories $O$ between the ortho-symplectic Lie superalgebras and classical Lie algebras of $BCD$ types. This provides a complete and conceptual solution of the irreducible character problem for the ortho-symplectic Lie superalgebras in a parabolic category $O$, which includes all finite-dimensional irreducible modules, in terms of classical Kazhdan-Lusztig polynomials.