For the algebraic group $SL\_n$ (type $A\_{n-1}$) and for a dominant weight $\lambda$ the standard monomials are indexed by the semi-standard young tableaux of shape $\lambda$ and they form a basis for the representation $V\_{\lambda}^\*$. For other types of simple algebraic groups do we have a description of standard monomials in terms of tableau ? If so, then how are the semi-standard young tableaux described ? A small example illustrating the basis elements say for $B\_4$ or $D\_5$ in terms of tableau will be highly appreciated. 



Standard Monomial basis for other types
Standard monomial theory has been extended to all classical groups by Lakshmibai, Seshadri and others in the series of papers "Geometry of $G/P$ I-IX".


A very concise description of standard tableaux in this setting can be found in the appendix of "Littelmann, Peter: A generalization of the Littlewood-Richardson rule. J. Algebra 130 (1990), no. 2, 328–368".


Note, that the standard monomial approach was later generalized er even superseded by Littelmann's path model and Kashiwara's crystals. These work even for symmetrizable Kac-Moody algebras.


