The Bernstein-Sato b-function for the complement of the open $S{L}_n$-orbit on a triple flag variety

We calculate Bernstein-Sato b-functions for $f_{G^3}^{\lambda }$, a $S{L}_n$-invariant section of a line bundle on $SL_n/B \times SL_n/B \times $\mathbb{P}$^{n - 1}$whosezero-setisthecomplementoftheopen$G$-diagonal orbit. The proof uses a similar calculation by Kashiwara of the b-function for $f^{\lambda }$, a $B^{-}$-semiinvariant section of a line bundle on $S{L}_n\mathrm{/}B$ whose zero-set is the complement of the big Bruhat cell.