JournalsprimsVol. 48, No. 1pp. 45–63

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
Super Duality and Homology of Unitarizable Modules of Lie Algebras cover
Download PDF

Abstract

The u\mathfrak u-homology formulas for unitarizable modules at negative levels over classical Lie algebras of infinite rank of types gl(n)\mathfrak gl (n), sp(2n)\mathfrak sp (2n) and so(2n)\mathfrak so (2n) are obtained. As a consequence, we recover the Enright's formulas for three Hermitian symmetric pairs of classical types (SU(p,q),SU(p)×SU(q))(SU(p,q),SU(p)\times SU(q)), (Sp(2n),U(n))(Sp(2n),U(n)) and (SO(2n),U(n))(SO^\ast(2n),U(n)).

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