Abstract:We study embeddings J → G of simple linear algebraic groups with the following property: the simple components of the J module Lie(G)/ Lie(J) are all minuscule representations of J. One family of examples occurs when the group G has roots of two different lengths and J is the subgroup generated by the long roots. We classify all such embeddings when J = SL 2 and J = SL 3 , show how each embedding implies the existence of exceptional algebraic structures on the graded components of Lie(G), and relate properties… Show more
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