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.
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