Super Duality and Homology of Unitarizable Modules of Lie Algebras

  • Po-Yi Huang

    National Cheng Kung University, Tainan, Taiwan
  • Ngau Lam

    National Cheng Kung University, Tainan, Taiwan
  • Tze-Ming To

    National Changhua University of Eduation, Taiwan

Abstract

The -homology formulas for unitarizable modules at negative levels over classical Lie algebras of infinite rank of types , and are obtained. As a consequence, we recover the Enright's formulas for three Hermitian symmetric pairs of classical types , and .

Cite this article

Po-Yi Huang, Ngau Lam, Tze-Ming To, Super Duality and Homology of Unitarizable Modules of Lie Algebras. Publ. Res. Inst. Math. Sci. 48 (2012), no. 1, pp. 45–63

DOI 10.2977/PRIMS/60