JournalsprimsVol. 44 , No. 4DOI 10.2977/prims/1231263785

Brundan–Kazhdan–Lusztig and Super Duality Conjectures

  • Shun-Jen Cheng

    Academia Sinica, Taipei, Taiwan
  • Weiqiang Wang

    University of Virginia, Charlottesville, USA
Brundan–Kazhdan–Lusztig and Super Duality Conjectures cover

Abstract

We formulate a general super duality conjecture on connections between parabolic categories O of modules over Lie superalgebras and Lie algebras of type A, based on a Fock space formalism of their Kazhdan–Lusztig theories which was initiated by Brundan. We show that the Brundan–Kazhdan–Lusztig (BKL) polynomials for gl(m|n) in our parabolic setup can be identified with the usual parabolic Kazhdan–Lusztig polynomials. We establish some special cases of the BKL conjecture on the parabolic category O of gl(m|n)-modules and additional results which support the BKL conjecture and super duality conjecture.