Japanese Journal of Mathematics

, Volume 7, Issue 1, pp 41–134

Denominator identities for finite-dimensional Lie superalgebras and Howe duality for compact dual pairs

  • Maria Gorelik
  • Victor G. Kac
  • Pierluigi Möseneder Frajria
  • Paolo Papi
Original Articles

DOI: 10.1007/s11537-012-1104-z

Cite this article as:
Gorelik, M., Kac, V.G., Möseneder Frajria, P. et al. Jpn. J. Math. (2012) 7: 41. doi:10.1007/s11537-012-1104-z

Abstract

We provide formulas for the denominator and superdenominator of a basic classical type Lie superalgebra for any set of positive roots. We establish a connection between certain sets of positive roots and the theory of reductive dual pairs of real Lie groups, and, as an application of these formulas, we recover the Theta correspondence for compact dual pairs. Along the way we give an explicit description of the real forms of basic classical type Lie superalgebras.

Keywords and phrases

Lie superalgebra denominator identity arc diagram Howe duality 

Mathematics Subject Classification (2010)

17B20 22E46 05E10 

Copyright information

© The Mathematical Society of Japan and Springer Japan 2012

Authors and Affiliations

  • Maria Gorelik
    • 1
  • Victor G. Kac
    • 2
  • Pierluigi Möseneder Frajria
    • 3
  • Paolo Papi
    • 4
  1. 1.Department of Mathematics, Faculty of Mathematics and Computer ScienceThe Weizmann Institute of ScienceRehovotIsrael
  2. 2.Department of MathematicsMITCambridgeUSA
  3. 3.Politecnico di Milano, Polo regionale di ComoComoItaly
  4. 4.Dipartimento di MatematicaSapienza Università di RomaRomaItaly