The Bernstein-Sato B-function for the Complement of the Open SLn -Orbit on a Triple Flag Variety

We calculate Bernstein-Sato b-functions for SLn -invariant sections of line bundles on SLn /B × SLn /B × Pn−1 whose zero-set is the complement of the open SLn -diagonal orbit. The proof uses a similar calculation by Kashiwara of the b-function for B − -semiinvariant sections of line bundles on SLn /B whose zero-set is the complement of the big Bruhat cell.