Small semisimple subalgebras of semisimple Lie algebras

Details Small semisimple subalgebras of semisimple Lie algebras Small semisimple subalgebras of semisimple Lie algebras

2004-08-23

arxiv.org/abs/math/0408302v1

Mathematics

Representation Theory

16 pages

Scientific paper

The main goal of this paper is to prove the following theorem: Let $\frak k$ be an $\frak {sl}_2$-subalgebra of a semisimple Lie algebra $\frak g$, none of whose simple factors is of type $A1$. Then there exists a positive integer $b(\frak k, \frak g)$, such that for every irreducible finite dimensional $\frak g$-module $V$, there exists an injection of $\frak k$-modules $W \to V$, where $W$ is an irreducible $\frak k$-module of dimension less than $b(\frak k, \frak g)$. This result was announced in math.RT/0310140.

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