# 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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