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