Schubert polynomials and Arakelov theory of orthogonal flag varieties

Harry Tamvakis

Published 2009-07-19, updated 2013-09-06Version 2

We propose a theory of combinatorially explicit Schubert polynomials which represent the Schubert classes in the Borel presentation of the cohomology ring of orthogonal flag varieties. We use these polynomials to describe the arithmetic Schubert calculus on these spaces. We also give a method to compute the natural arithmetic intersection numbers which arise, and prove that they are all rational numbers.