On Reidemeister torsion of flag manifolds of compact semisimple Lie groups

Abstract

In this paper we calculate Reidemeister torsion of flag manifold K/T of compact semi-simple Lie group K = SUn+1 using Reidemeister torsion formula and Schubert calculus, where T is maximal torus of K. We find that this number is 1. Also we explicitly calculate ring structure of integral cohomology algebra of flag manifold K/T of compact semi-simple Lie group K = SUn+1 using root data, and Groebner basis techniques.