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

Abstract

We calculate Bernstein-Sato b-functions for $f_{G^3}^{\lambda }$, a $S{L}_n$-invariant section of a line bundle on $S{L}_n/B\times S{L}_n/B\times {\mathbb{P}}^{n-1}$ whose zero-set is the complement of the open $G$-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 $S{L}_n/B$ whose zero-set is the complement of the big Bruhat cell.

References in corpus (2)

• Symplectic reflection algebras, Calogero-Moser space, and deformed Harish-Chandra homomorphism
• On mirabolic D-modules