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On Reidemeister torsion of flag manifolds of compact semisimple Lie groups. (English) Zbl 1484.57023

Summary: 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.

MSC:

57Q10 Simple homotopy type, Whitehead torsion, Reidemeister-Franz torsion, etc.
14M15 Grassmannians, Schubert varieties, flag manifolds
14N15 Classical problems, Schubert calculus
16Z10 Gröbner-Shirshov bases
22E46 Semisimple Lie groups and their representations
22E67 Loop groups and related constructions, group-theoretic treatment
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References:

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