About: Standard monomial theory

In algebraic geometry, standard monomial theory describes the sections of a line bundle over a generalized flag variety or Schubert variety of a reductive algebraic group by giving an explicit basis of elements called standard monomials. Many of the results have been extended to Kac–Moody algebras and their groups. There are monographs on standard monomial theory by and and survey articles by V. Lakshmibai, C. Musili, and C. S. Seshadri and V. Lakshmibai and C. S. Seshadri One of important open problems is to give a completely geometric construction of the theory.