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 $K=SU_{n+1}$ 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 $K=SU_{n+1 }$ using root data, and Groebner basis techniques.

Keywords

• reidemeister torsion
• flag manifolds
• weyl groups
• schubert calculus
• groebner-shirshov bases
• graded inverse lexicographic order