Abstract
We define and classify splints of root systems of complex semisimple Lie algebras. In a few instances, splints play a role in determining branching rules of a module over a complex semisimple Lie algebra when restricted to a subalgebra. In these particular cases, the set of submodules with respect to the subalgebra themselves may be regarded as the character of an auxiliary Lie algebra which may or may not be another Lie subalgebra.
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References
Billey S., Postnikov A.: Smoothness in Schubert varieties via patterns in root subsystems. Adv. Appl. Math. 34, 447–466 (2005)
Fronsdal, C.: Group theory and applications to particle physics. Elementary particle physics and field theory (Brandeis Summer Institute), vol. 1, pp. 427– 532 (1962)
Fulton W., Harris J.: Representation Theory. Springer, New York (1991)
Heckman G.J.: Projections of orbits and asymptotic behavior of multiplicities for compact connected Lie groups. Inv. Math. 67, 333–356 (1982)
Humphreys J.E.: Reflection Groups and Coxeter Groups. Cambridge University Press, Cambridge (1992)
Jacobson N.: Lie Algebras. Dover, New York (1979)
King R.C., Qubanchi A.H.A.: The evaluation of weight multiplicities of G 2. J. Phys. A 11, 1491–1499 (1978)
Lyakhovsky V.D., Melnikov S.Y.: Recursion relations and branching rules for simple Lie algebras. J. Phys. A 29, 1075–1087 (1996)
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Richter, D.A. Splints of classical root systems. J. Geom. 103, 103–117 (2012). https://doi.org/10.1007/s00022-012-0109-3
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DOI: https://doi.org/10.1007/s00022-012-0109-3