Brundan–Kazhdan–Lusztig and Super Duality Conjectures

  • Shun-Jen Cheng

    Academia Sinica, Taipei, Taiwan
  • Weiqiang Wang

    University of Virginia, Charlottesville, USA


We formulate a general super duality conjecture on connections between parabolic categories of modules over Lie superalgebras and Lie algebras of type , 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 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 of -modules and additional results which support the BKL conjecture and super duality conjecture.

Cite this article

Shun-Jen Cheng, Weiqiang Wang, Brundan–Kazhdan–Lusztig and Super Duality Conjectures. Publ. Res. Inst. Math. Sci. 44 (2008), no. 4, pp. 1219–1272

DOI 10.2977/PRIMS/1231263785