For a finite Coxeter system and a subset of its diagram nodes, we define spherical elements (a generalization of Coxeter elements). Conjecturally, for Weyl groups, spherical elements index Schubert varieties in a flag manifold G/B that are spherical for the action of a Levi subgroup. We evidence the conjecture, employing the combinatorics of Demazure modules, and work of R. Avdeev and A. Petukhov, M. Can and R. Hodges, R. Hodges and V. Lakshmibai, P. Karuppuchamy, P. Magyar and J. Weyman and A. Zelevinsky, N. Perrin, J. Stembridge, and B. Tenner. In type A, we establish connections with the key polynomials of A. Lascoux and M.-P. Schützenberger, multiplicity-freeness, and split-symmetry in algebraic combinatorics. Thereby, we invoke theorems of A. Kohnert, V. Reiner and M. Shimozono, and C. Ross and A. Yong.
1
Dept. of Mathematics, University of California at San Diego, La Jolla, U.S.A.
2
Dept. of Mathematics, University of Illinois, Urbana-Champaign, U.S.A.
Reuven Hodges; Alexander Yong. Coxeter Combinatorics and Spherical Schubert Geometry. Journal of Lie Theory, Tome 32 (2022) no. 2, pp. 447-474. http://geodesic.mathdoc.fr/item/JOLT_2022_32_2_a6/
@article{JOLT_2022_32_2_a6,
author = {Reuven Hodges and Alexander Yong},
title = {Coxeter {Combinatorics} and {Spherical} {Schubert} {Geometry}},
journal = {Journal of Lie Theory},
pages = {447--474},
year = {2022},
volume = {32},
number = {2},
url = {http://geodesic.mathdoc.fr/item/JOLT_2022_32_2_a6/}
}
TY - JOUR
AU - Reuven Hodges
AU - Alexander Yong
TI - Coxeter Combinatorics and Spherical Schubert Geometry
JO - Journal of Lie Theory
PY - 2022
SP - 447
EP - 474
VL - 32
IS - 2
UR - http://geodesic.mathdoc.fr/item/JOLT_2022_32_2_a6/
ID - JOLT_2022_32_2_a6
ER -
%0 Journal Article
%A Reuven Hodges
%A Alexander Yong
%T Coxeter Combinatorics and Spherical Schubert Geometry
%J Journal of Lie Theory
%D 2022
%P 447-474
%V 32
%N 2
%U http://geodesic.mathdoc.fr/item/JOLT_2022_32_2_a6/
%F JOLT_2022_32_2_a6
