On Reidemeister torsion of flag manifolds of compact semisimple Lie groups

Ozel C., Basbaydar H., SÖZEN Y., YILMAZ E., Lee J. R., Park C.

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

  • Publication Type: Article / Article
  • Volume: 5 Issue: 6
  • Publication Date: 2020
  • Doi Number: 10.3934/math.2020484
  • Journal Name: AIMS MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.7562-7581
  • Hacettepe University Affiliated: Yes

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.