Masaharu Kaneda
Osaka University, Japan
On the Frobenius direct image of the structure sheaf of the flag variety.
Abstract: Let F_*\mathcal{O}_{G/B} be the direct image of the structure sheaf \mathcal{O}_{G/B} of the flag variety G/B under the Frobenius endomorphism F on G/B, or more generally on G/P with P a parabolic subgroup of G. The endomorphism ring of F_*\mathcal{O}_{G/B} is the first term in the p-filtration of the sheaf of rings of differential operators on G/B and is also a central reduction of the sheaf of the arithmetic differential operators on G/B of level 0. Together with Ye Jiachen I found in case G is of rank at most 2 and also in case G/P is a projective space that F_*\mathcal{O}_{G/B} provides a tilting sheaf on G/P.