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I've got a couple rather geometric questions about the following setup. Let $X$ be a scheme over an algebraically closed field ($\mathbb{C}$, say) with the action of a torus $T$, such that the action …

Let $G$ be a semisimple algebraic group over $\mathbb{C}$ and for a highest weight $\lambda$, denote by $V_{\lambda}^w$ the Demazure module associated with $\lambda$ and $w$. More precisely, $V_{\lamb …

I am interested in two related constructions which give us either the cohomology or the $T \times \mathbb{C}^*$-equivariant $K$-theory of flag varieties. Let $G$ be a semisimple, simply connected alg …

The confusing part here is that there is a subtlety when one passes from characters to line bundles. Let $\lambda$ be a dominant character of T. Consider the line bundle L given by $G \times_B \mathbb …