Abstract
The paper deals with the real classical Lie algebras and their finite dimensional irreducible representations. Signature formulae for Hermitian forms invariant relative to these representations are considered. It is possible to associate with the irreducible representation a Hurwitz matrix of special kind. So the calculation of the signatures is reduced to the calculation of Hurwitz determinants. Hence it is possible to use the Routh algorithm for the calculation.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
F.I. Karpelevich: “Simple subalgebras of real Lie algebras”, Trudy Mosk. Mat. Obshch., Vol. 4, (1955), pp. 3–112.
J. Patera and R.T. Sharp: “Signatures of finite su representations”, J. Math. Phys., Vol. 25, (1984), pp. 2128–2131, MR0748387 (85j:22042).
A.N. Rudy: “Signatures of finite representation of real, simple Lie algebras”, J. Phys. A: Math. Gen., Vol. 26, (1993), pp. 5873–5880, MR1252794(94i:17014).
A.N. Rudy: “Signatures of finite classical Lie algebra representations”, J. Phys. A:Math. Gen., Vol. 28 (1995), pp. 1641–1653, MR1338050(96e:17017).
N. Burbaki: Groupes et algebras de Lie. Ch. IV–VI, Hermann, Paris, 1968.
F.R. Gantmacher: The theory of matrices, AMS Chelsea Publishing, Providence, RI, 1959.
Author information
Authors and Affiliations
About this article
Cite this article
Rudy, A.N. The Hurwitz determinants and the signatures of irreducible representations of simple real Lie algebras. centr.eur.j.math. 3, 606–613 (2005). https://doi.org/10.2478/BF02475621
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.2478/BF02475621