Type B Richardson-clan conjecture

Let $u$ and $v$ be type $B$ Weyl group elements satisfying the conditions in the paper's Bruhat-comparability lemma. Associate to them a symmetric clan $\gamma(u,v)$ by the five cases described in the source: cases (1)–(3) produce clans for which $X_u^v$ and $X_{w_0v}^{w_0u}$ are the two distinct $L$-orbit closures associated to the clan, while cases (4)–(5) produce a clan for which $X_u^v$ is the single associated $L$-orbit closure.

Type B Richardson-clan conjecture. With these definitions, in cases (1)–(3), $X_u^v$ is one of the two $L$-orbit closures associated to $\gamma(u,v)$ and $X_{w_0v}^{w_0u}$ is the other; in cases (4)–(5), $X_u^v$ is the single $L$-orbit closure associated to $\gamma(u,v)$.

The claim identifies Richardson varieties with orbit closures and is used to derive a Schubert-calculus rule for the relevant structure constants. The supplied text gives no resolution evidence.