AIMS MATHEMATICS, vol.5, no.6, pp.7562-7581, 2020 (SCI-Expanded)
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.