The Hurwitz determinants and the signatures of irreducible representations of simple real Lie algebras
Open Mathematics (2005)
- Volume: 3, Issue: 4, page 606-613
- ISSN: 2391-5455
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topAlexander Rudy. "The Hurwitz determinants and the signatures of irreducible representations of simple real Lie algebras." Open Mathematics 3.4 (2005): 606-613. <http://eudml.org/doc/268794>.
@article{AlexanderRudy2005,
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.},
author = {Alexander Rudy},
journal = {Open Mathematics},
keywords = {17B10; 17B20},
language = {eng},
number = {4},
pages = {606-613},
title = {The Hurwitz determinants and the signatures of irreducible representations of simple real Lie algebras},
url = {http://eudml.org/doc/268794},
volume = {3},
year = {2005},
}
TY - JOUR
AU - Alexander Rudy
TI - The Hurwitz determinants and the signatures of irreducible representations of simple real Lie algebras
JO - Open Mathematics
PY - 2005
VL - 3
IS - 4
SP - 606
EP - 613
AB - 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.
LA - eng
KW - 17B10; 17B20
UR - http://eudml.org/doc/268794
ER -
References
top- [1] F.I. Karpelevich: “Simple subalgebras of real Lie algebras”, Trudy Mosk. Mat. Obshch., Vol. 4, (1955), pp. 3–112. Zbl0068.26203
- [2] J. Patera and R.T. Sharp: “Signatures of finite su representations”, J. Math. Phys., Vol. 25, (1984), pp. 2128–2131, MR0748387 (85j:22042). http://dx.doi.org/10.1063/1.526420 Zbl0552.22011
- [3] 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). http://dx.doi.org/10.1088/0305-4470/26/21/025 Zbl0808.17001
- [4] A.N. Rudy: “Signatures of finite classical Lie algebra representations”, J. Phys. A:Math. Gen., Vol. 28 (1995), pp. 1641–1653, MR1338050(96e:17017). http://dx.doi.org/10.1088/0305-4470/28/6/018 Zbl0862.17003
- [5] N. Burbaki: Groupes et algebras de Lie. Ch. IV–VI, Hermann, Paris, 1968.
- [6] F.R. Gantmacher: The theory of matrices, AMS Chelsea Publishing, Providence, RI, 1959. Zbl0085.01001
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