Geodesic
Chevalley-Monk and Giambelli formulas for Peterson Varieties
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AT, 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014), DMTCS Proceedings vol. AT, 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014) (2014).

Voir la notice de l'article provenant de la source Episciences

A Peterson variety is a subvariety of the flag variety $G/B$ defined by certain linear conditions. Peterson varieties appear in the construction of the quantum cohomology of partial flag varieties and in applications to the Toda flows. Each Peterson variety has a one-dimensional torus $S^1$ acting on it. We give a basis of Peterson Schubert classes for $H_{S^1}^*(Pet)$ and identify the ring generators. In type A Harada-Tymoczko gave a positive Monk formula, and Bayegan-Harada gave Giambelli's formula for multiplication in the cohomology ring. This paper gives a Chevalley-Monk rule and Giambelli's formula for all Lie types. 
@article{DMTCS_2014_special_265_a74,
     author = {Drellich, Elizabeth},
     title = {Chevalley-Monk and {Giambelli} formulas for {Peterson} {Varieties}},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AT, 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014)},
     year = {2014},
     doi = {10.46298/dmtcs.2449},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2449/}
}
TY  - JOUR
AU  - Drellich, Elizabeth
TI  - Chevalley-Monk and Giambelli formulas for Peterson Varieties
JO  - Discrete mathematics & theoretical computer science
PY  - 2014
VL  - DMTCS Proceedings vol. AT, 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014)
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2449/
DO  - 10.46298/dmtcs.2449
LA  - en
ID  - DMTCS_2014_special_265_a74
ER  - 
%0 Journal Article
%A Drellich, Elizabeth
%T Chevalley-Monk and Giambelli formulas for Peterson Varieties
%J Discrete mathematics & theoretical computer science
%D 2014
%V DMTCS Proceedings vol. AT, 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014)
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2449/
%R 10.46298/dmtcs.2449
%G en
%F DMTCS_2014_special_265_a74
Drellich, Elizabeth. Chevalley-Monk and Giambelli formulas for Peterson Varieties. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AT, 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014), DMTCS Proceedings vol. AT, 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014) (2014). doi : 10.46298/dmtcs.2449. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2449/

Cité par Sources :