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.
Classification :
05A05, 14M15, 17B22, 57T15
Mots-clés :
Real flag manifolds, symmetric group, root systems, Schubert cells, homology
Affiliations des auteurs :
Jordan Lambert
1
;
Lonardo Rabelo
2
1
Dept. of Mathematics, ICEx, Universidade Federal Fluminense, Volta Redonda, Brazil
2
Dept. of Mathematics, Federal University of Juiz de Fora, Brazil
Jordan Lambert; Lonardo Rabelo. A Correspondence Between Boundary Coefficients of Real Flag Manifolds and Height of Roots. Journal of Lie Theory, Tome 32 (2022) no. 2, pp. 431-446. http://geodesic.mathdoc.fr/item/JOLT_2022_32_2_a5/
@article{JOLT_2022_32_2_a5,
author = {Jordan Lambert and Lonardo 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},
url = {http://geodesic.mathdoc.fr/item/JOLT_2022_32_2_a5/}
}
TY - JOUR
AU - Jordan Lambert
AU - Lonardo Rabelo
TI - A Correspondence Between Boundary Coefficients of Real Flag Manifolds and Height of Roots
JO - Journal of Lie Theory
PY - 2022
SP - 431
EP - 446
VL - 32
IS - 2
UR - http://geodesic.mathdoc.fr/item/JOLT_2022_32_2_a5/
ID - JOLT_2022_32_2_a5
ER -
%0 Journal Article
%A Jordan Lambert
%A Lonardo Rabelo
%T A Correspondence Between Boundary Coefficients of Real Flag Manifolds and Height of Roots
%J Journal of Lie Theory
%D 2022
%P 431-446
%V 32
%N 2
%U http://geodesic.mathdoc.fr/item/JOLT_2022_32_2_a5/
%F JOLT_2022_32_2_a5
