Geodesic
Combinatorics of symplectic invariant tensors
Discrete mathematics & theoretical computer science, DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015), DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015) (2015).

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

An important problem from invariant theory is to describe the subspace of a tensor power of a representation invariant under the action of the group. According to Weyl's classic, the first main (later: 'fundamental') theorem of invariant theory states that all invariants are expressible in terms of a finite number among them, whereas a second main theorem determines the relations between those basic invariants.Here we present a transparent, combinatorial proof of a second fundamental theorem for the defining representation of the symplectic group $Sp(2n)$. Our formulation is completely explicit and provides a very precise link to $(n+1)$-noncrossing perfect matchings, going beyond a dimension count. As a corollary, we obtain an instance of the cyclic sieving phenomenon. 
@article{DMTCS_2015_special_285_a52,
     author = {Rubey, Martin and Westbury, Bruce W.},
     title = {Combinatorics of symplectic invariant tensors},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015)},
     year = {2015},
     doi = {10.46298/dmtcs.2508},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2508/}
}
TY  - JOUR
AU  - Rubey, Martin
AU  - Westbury, Bruce W.
TI  - Combinatorics of symplectic invariant tensors
JO  - Discrete mathematics & theoretical computer science
PY  - 2015
VL  - DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015)
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2508/
DO  - 10.46298/dmtcs.2508
LA  - en
ID  - DMTCS_2015_special_285_a52
ER  - 
%0 Journal Article
%A Rubey, Martin
%A Westbury, Bruce W.
%T Combinatorics of symplectic invariant tensors
%J Discrete mathematics & theoretical computer science
%D 2015
%V DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015)
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2508/
%R 10.46298/dmtcs.2508
%G en
%F DMTCS_2015_special_285_a52
Rubey, Martin; Westbury, Bruce W. Combinatorics of symplectic invariant tensors. Discrete mathematics & theoretical computer science, DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015), DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015) (2015). doi : 10.46298/dmtcs.2508. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2508/

Cité par Sources :