Introduction to the flag variety

Title:  Introduction to the flag variety

Abstract:  Following Fulton's treatment in his book Young Tableaux, I will define the flag variety F_n (for the general linear group GL_n) and give explicit defining equations for it.  Using Young tableaux, I will show how these relations lead naturally to a realization of all finite-dimensional polynomial representations of this group, showing how these appear in the coordinate ring of F_n.  I will also briefly indicate how the equations generalize to other classical (i.e., symplectic and orthogonal) groups.