Abstract
The aim of this Letter is to characterize the representations of Euclidean Kač-Moody with highest weight, spanned by the principal subalgebra action on a highest-weight vector.
We conjecture that, modulo the Dynkin diagram automorphisms, only the basic representations have this property. This is proved for A sup(1)infn , D sup(1)inf4 , and A sup(2)inf2 .
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References
Kač, V. G., Kazdhan, D. A., Lepowsky, J., and Wilson, R. L., ‘Realization of the Basic Representations of the Euclidean Lie Algebras’, Adv. Math. 42, No. 1 (1981).
KačV. G., Infinite Dimensional Lie Algebras, Progress in Mathematics, Vol. 44, Birkhäuser, Basle, 1983.
Lepowsky, J. and Wilson, R. L., ‘Construction of the Affine Lie Algebra A (1)1 ’, Commun. Math. Phys. 62, No. 1 (1978).
Bausch, J., ‘Etude et classification des automorphismes d'ordre fini et de 1re espèce des algèbres de Kač-Moody affines’, Thèse de l'Université de Nancy I, 1985.
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Ammar, M.B., Selmi, M. Highest weight representations of Euclidean Kac-Moody algebras spanned by the principal subalgebra action. Letters in Mathematical Physics 12, 343–356 (1986). https://doi.org/10.1007/BF00402668
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DOI: https://doi.org/10.1007/BF00402668