Abstract
While Hodge is the founder of classical Standard Monomial Theory, Seshadri is the founder of modern Standard Monomial Theory. In [7, 8], Hodge constructed a nice basis for the coordinate ring of a Grassmann variety (as well as a Schubert subvariety) for its canonical Plucker imbedding in a projective space. The basis is indexed by “standard Young tableaux”. The modern Standard Monomial Theory was initiated by Seshadri in the early 1970’s. The aim of Standard Monomial Theory (SMT) is the construction of nice bases of the spaces of sections of line bundles on the generalized flag variety as well as its Schubert varieties, in particular bases for finite dimensional representations of a semisimple algebraic group. SMT has led to very many developments in the areas of Combinatorics, Algebraic Geometry, Representation Theory, Quantum Groups, etc. We shall now give a brief account of the development of this theory; this could be broken into the following phases.
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