Geodesic
Representations on Hessenberg Varieties and Young's Rule
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011), DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011) (2011).

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

We combinatorially construct the complex cohomology (equivariant and ordinary) of a family of algebraic varieties called regular semisimple Hessenberg varieties. This construction is purely in terms of the Bruhat order on the symmetric group. From this a representation of the symmetric group on the cohomology is defined. This representation generalizes work of Procesi, Stembridge and Tymoczko. Here a partial answer to an open question of Tymoczko is provided in our two main result. The first states, when the variety has multiple connected components, this representation is made up by inducing through a parabolic subgroup of the symmetric group. Using this, our second result obtains, for a special family of varieties, an explicit formula for this representation via Young's rule, giving the multiplicity of the irreducible representations in terms of the classical Kostka numbers. 
@article{DMTCS_2011_special_260_a76,
     author = {Teff, Nicholas},
     title = {Representations on {Hessenberg} {Varieties} and {Young's} {Rule}},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011)},
     year = {2011},
     doi = {10.46298/dmtcs.2963},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2963/}
}
TY  - JOUR
AU  - Teff, Nicholas
TI  - Representations on Hessenberg Varieties and Young's Rule
JO  - Discrete mathematics & theoretical computer science
PY  - 2011
VL  - DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011)
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2963/
DO  - 10.46298/dmtcs.2963
LA  - en
ID  - DMTCS_2011_special_260_a76
ER  - 
%0 Journal Article
%A Teff, Nicholas
%T Representations on Hessenberg Varieties and Young's Rule
%J Discrete mathematics & theoretical computer science
%D 2011
%V DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011)
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2963/
%R 10.46298/dmtcs.2963
%G en
%F DMTCS_2011_special_260_a76
Teff, Nicholas. Representations on Hessenberg Varieties and Young's Rule. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011), DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011) (2011). doi : 10.46298/dmtcs.2963. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2963/

Cité par Sources :