A two-dimensional pictorial presentation of Berele's insertion algorithm for symplectic tableaux
The electronic journal of combinatorics, Tome 12 (2005)
Voir la notice de l'article provenant de la source The Electronic Journal of Combinatorics website
Zbl arXiv EuDML
We give the first two-dimensional pictorial presentation of Berele's correspondence, an analogue of the Robinson-Schensted (R-S) correspondence for the symplectic group $Sp(2n, {\Bbb C})$. From the standpoint of representation theory, the R-S correspondence combinatorially describes the irreducible decomposition of the tensor powers of the natural representation of $GL(n,{\Bbb C})$. Berele's insertion algorithm gives the bijection that describes the irreducible decomposition of the tensor powers of the natural representation of $Sp(2n,{\Bbb C})$. Two-dimensional pictorial presentations of the R-S correspondence via local rules (first given by S. Fomin) and its many variants have proven very useful in understanding their properties and creating new generalizations. We hope our new presentation will be similarly useful.
Tom Roby; Itaru Terada. A two-dimensional pictorial presentation of Berele's insertion algorithm for symplectic tableaux. The electronic journal of combinatorics, Tome 12 (2005). doi: 10.37236/1901
@article{10_37236_1901,
author = {Tom Roby and Itaru Terada},
title = {A two-dimensional pictorial presentation of {Berele's} insertion algorithm for symplectic tableaux},
journal = {The electronic journal of combinatorics},
year = {2005},
volume = {12},
doi = {10.37236/1901},
zbl = {1068.05070},
url = {http://geodesic.mathdoc.fr/articles/10.37236/1901/}
}
TY - JOUR AU - Tom Roby AU - Itaru Terada TI - A two-dimensional pictorial presentation of Berele's insertion algorithm for symplectic tableaux JO - The electronic journal of combinatorics PY - 2005 VL - 12 UR - http://geodesic.mathdoc.fr/articles/10.37236/1901/ DO - 10.37236/1901 ID - 10_37236_1901 ER -
Cité par Sources :