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

J. Lambert; L. Rabelo

doi:10.5802/jolt.1237

J. Lambert; L. Rabelo

Journal of Lie Theory, Volume 32 (2022) no. 2, pp. 431-446

Abstract

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.

arXiv Zbl

DOI: 10.5802/jolt.1237

Classification: 05A05, 14M15, 17B22, 57T15
Keywords: Real flag manifolds, symmetric group, root systems, Schubert cells, homology

@article{JOLT_2022_32_2_a5,
     author = {J. Lambert and L. Rabelo},
     title = {A {Correspondence} {Between} {Boundary} {Coefficients} of {Real} {Flag} {Manifolds} and {Height} of {Roots}},
     journal = {Journal of Lie Theory},
     pages = {431--446},
     year = {2022},
     volume = {32},
     number = {2},
     doi = {10.5802/jolt.1237},
     zbl = {1485.57031},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1237/}
}

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J. Lambert; L. Rabelo. A Correspondence Between Boundary Coefficients of Real Flag Manifolds and Height of Roots. Journal of Lie Theory, Volume 32 (2022) no. 2, pp. 431-446. doi: 10.5802/jolt.1237

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