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Journal of Lie Theory 28 (2018), No. 4, 915--940
Copyright Heldermann Verlag 2018

Extending Generalized Spin Representations

Robin Lautenbacher
Institut für Theoretische Physik, Fachbereich 7, J.-Liebig-Universität, Heinrich-Buff-Ring 16, 35392 Giessen, Germany

Ralf Köhl
Mathematisches Institut, Fachbereich 7, J.-Liebig-Universität, Arndtstrasse 2, 35392 Giessen, Germany

We revisit the construction of higher spin representations by Kleinschmidt and Nicolai for E10, generalize it to arbitrary simply laced types, and provide a coordinate-free approach to the (3/2)-spin and (5/2)-spin representations. Moreover, we discuss the relationship between our findings and the representation theory of Sym3 pointed out to us by Levy.

Keywords: Simply laced real Kac-Moody algebra, spin representation.

MSC: 17B67, 81R10

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