Let $k$ be a field of characteristic zero, $G$ be a reductive group with a Borel $B$ and $\mathcal{F}:=G/B$ the associated flag variety. Let $W$ be the Weyl-group of G.

Then let $S \subset W$ and $Z=\bigcup_{w \in S} C(w)$ where $C(w)=BwB/B$ is the Schubert cell associated to $w$.

I'm interested to know when $Z$ is an affine scheme. This is for example the case if all $w \in S$ have the same length. Is this the only case?

Let $k$ be a field of characteristic zero, $G$ be a reductive group with a Borel $B$ and $\mathcal{F}:=G/B$ the associated flag variety. Let $W$ be the Weyl-group of G.

Then let $S \subset W$ and $Z=\bigcup_{w \in S} C(w) \subset \mathcal{F}$ where $C(w)=BwB/B$ is the Schubert cell associated to $w$.

I'm interested to know when $Z$ is an affine scheme. This is for example the case if all $w \in S$ have the same length. Is this the only case?

Let $k$ be a field of characteristic zero, $G$ be a reductive group with a Borel $B$ and $\mathcal{F}:=G/B$ the associated flag variety. Let W be the Weyl-group of G.

Then let $S \subset W$ and $Z=\cup_{w \in S} C(w)$ where $C(w)=BwB/B$ is the Schubert cell associated to $w$.

I'm interested to know when Z is an affine scheme. This is for example the case if all $w \in S$ have the same length. Is this the only case?

Let $k$ be a field of characteristic zero, $G$ be a reductive group with a Borel $B$ and $\mathcal{F}:=G/B$ the associated flag variety. Let $W$ be the Weyl-group of G.

Then let $S \subset W$ and $Z=\bigcup_{w \in S} C(w)$ where $C(w)=BwB/B$ is the Schubert cell associated to $w$.

I'm interested to know when $Z$ is an affine scheme. This is for example the case if all $w \in S$ have the same length. Is this the only case?