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

The Bernstein-Sato b-function for the complement of the open $SL_n$-orbit on a triple flag variety