Standard Monomial Theory for Bott–Samelson Varieties of $\text{GL}(n)$

Abstract

We construct an explicit basis for the coordinate ring of the Bott–Samelson variety $Z_i$ associated to $G=\text{GL}(n)$ and an arbitrary sequence of simple reflections $\mathbf{i}$. Our basis is parametrized by certain standard tableaux and generalizes the Standard Monomial basis for Schubert varieties.