A Bruhat atlas for the Mehta-van der Kallen stratification of $T^* GL_n/B$

Abstract

Mehta and van der Kallen put a Frobenius splitting on the type A cotangent bundle T * GL n /B, thereby defining a stratification by compatibly split subvarieties, and they determined a few of the elements of this stratification. We embed T * GL n /B as a stratum in a larger stratified (and Frobenius split) space GL n /B × Mat n whose stratification we determine, thereby giving a full description of the one of Mehta-van der Kallen. The main technique is to endow GL n /B × Mat n with a Bruhat atlas, covering it with open sets that are stratified-isomorphic to Bruhat cells (in GL 2n /B 2n ).