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Journal of Lie Theory 32 (2022), No. 2, 431--446
Copyright Heldermann Verlag 2022

A Correspondence Between Boundary Coefficients of Real Flag Manifolds and Height of Roots

Jordan Lambert
Dept. of Mathematics, ICEx, Universidade Federal Fluminense, Volta Redonda, Brazil

Lonardo Rabelo
Dept. of Mathematics, Federal University of Juiz de Fora, Brazil

We prove a new formula for the cellular homology coefficients of real flag manifolds in terms of the height of certain roots. For real flag manifolds of type A, we get simple expressions for the coefficients that allow us to compute the first and second integral homology groups exhibiting their generators.

Keywords: Real flag manifolds, symmetric group, root systems, Schubert cells, homology.

MSC: 05A05, 14M15, 17B22, 57T15.

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