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Generalized spin representations

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Generalized spin representations. / Hainke, Guntram; Koehl, Ralf; Levy, Paul.
In: Muenster Journal of Mathematics, 2015.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Hainke, G, Koehl, R & Levy, P 2015, 'Generalized spin representations', Muenster Journal of Mathematics. https://doi.org/10.17879/65219674985

APA

Hainke, G., Koehl, R., & Levy, P. (2015). Generalized spin representations. Muenster Journal of Mathematics. https://doi.org/10.17879/65219674985

Vancouver

Hainke G, Koehl R, Levy P. Generalized spin representations. Muenster Journal of Mathematics. 2015. Epub 2015 Mar 25. doi: 10.17879/65219674985

Author

Hainke, Guntram ; Koehl, Ralf ; Levy, Paul. / Generalized spin representations. In: Muenster Journal of Mathematics. 2015.

Bibtex

@article{c32c2e3a39264267830b2e4028d8919b,
title = "Generalized spin representations",
abstract = "We introduce the notion of a generalized spin representation of the maximal compact subalgebra $\mathfrak k$ of a symmetrizable Kac--Moody algebra $\mathfrak g$ in order to show that, if defined over a formally real field, every such $\mathfrak k$ has a non-trivial reductive finite-dimensional quotient. The appendix illustrates how to compute the isomorphism types of these quotients for the real $E_n$ series. In passing this provides an elementary way of determining the isomorphism types of the maximal compact subalgebras of the semisimple split real Lie algebras of types $E_6$, $E_7$, $E_8$.",
author = "Guntram Hainke and Ralf Koehl and Paul Levy",
year = "2015",
doi = "10.17879/65219674985",
language = "English",
journal = "Muenster Journal of Mathematics",
issn = "1867-5778",

}

RIS

TY - JOUR

T1 - Generalized spin representations

AU - Hainke, Guntram

AU - Koehl, Ralf

AU - Levy, Paul

PY - 2015

Y1 - 2015

N2 - We introduce the notion of a generalized spin representation of the maximal compact subalgebra $\mathfrak k$ of a symmetrizable Kac--Moody algebra $\mathfrak g$ in order to show that, if defined over a formally real field, every such $\mathfrak k$ has a non-trivial reductive finite-dimensional quotient. The appendix illustrates how to compute the isomorphism types of these quotients for the real $E_n$ series. In passing this provides an elementary way of determining the isomorphism types of the maximal compact subalgebras of the semisimple split real Lie algebras of types $E_6$, $E_7$, $E_8$.

AB - We introduce the notion of a generalized spin representation of the maximal compact subalgebra $\mathfrak k$ of a symmetrizable Kac--Moody algebra $\mathfrak g$ in order to show that, if defined over a formally real field, every such $\mathfrak k$ has a non-trivial reductive finite-dimensional quotient. The appendix illustrates how to compute the isomorphism types of these quotients for the real $E_n$ series. In passing this provides an elementary way of determining the isomorphism types of the maximal compact subalgebras of the semisimple split real Lie algebras of types $E_6$, $E_7$, $E_8$.

U2 - 10.17879/65219674985

DO - 10.17879/65219674985

M3 - Journal article

JO - Muenster Journal of Mathematics

JF - Muenster Journal of Mathematics

SN - 1867-5778

ER -