Abstract
We describe a procedure for constructing monomial bases for finite dimensional irreducible representations of complex semisimple Lie algebras. A basis is calledmonomial if each of its elements is the result of applying to a (fixed) highest weight vector a monomial in the Chevalley basis elementsY α, α a simple root, in the opposite Borel subalgebra. As an immediate application we obtain a new proof of the main theorem of standard monomial theory for classical groups.
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Raghavan, K.N., Sankaran, P. A new approach to standard monomial theory for classical groups. Transformation Groups 3, 57–73 (1998). https://doi.org/10.1007/BF01237840
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DOI: https://doi.org/10.1007/BF01237840