Geodesic
On changing highest weight theories for finite $W$-algebras
Journal of Algebraic Combinatorics, Tome 37 (2013) no. 1, pp. 87-116.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: A highest weight theory for a finite W-algebra $U(\mathfrak{g},e)$ was developed in Brundan et al. (Int. Math. Res. Not. 15:rnn051, 2008). This leads to a strategy for classifying the irreducible finite dimensional $U(\mathfrak{g},e)$ -modules. The highest weight theory depends on the choice of a parabolic subalgebra of $\mathfrak{g}$ leading to different parameterizations of the finite dimensional irreducible $U(\mathfrak{g},e)$ -modules. We explain how to construct an isomorphism preserving bijection between the parameterizing sets for different choices of parabolic subalgebra when $\mathfrak{g}$ is of type A, or when $\mathfrak{g}$ is of types C or D and e is an even multiplicity nilpotent element.
Keywords: finite W-algebras, representation theory 
@article{JAC_2013__37_1_a3,
     author = {Brown, Jonathan and Goodwin, Simon M.},
     title = {On changing highest weight theories for finite $W$-algebras},
     journal = {Journal of Algebraic Combinatorics},
     pages = {87--116},
     publisher = {mathdoc},
     volume = {37},
     number = {1},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JAC_2013__37_1_a3/}
}
TY  - JOUR
AU  - Brown, Jonathan
AU  - Goodwin, Simon M.
TI  - On changing highest weight theories for finite $W$-algebras
JO  - Journal of Algebraic Combinatorics
PY  - 2013
SP  - 87
EP  - 116
VL  - 37
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JAC_2013__37_1_a3/
LA  - en
ID  - JAC_2013__37_1_a3
ER  - 
%0 Journal Article
%A Brown, Jonathan
%A Goodwin, Simon M.
%T On changing highest weight theories for finite $W$-algebras
%J Journal of Algebraic Combinatorics
%D 2013
%P 87-116
%V 37
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JAC_2013__37_1_a3/
%G en
%F JAC_2013__37_1_a3
Brown, Jonathan; Goodwin, Simon M. On changing highest weight theories for finite $W$-algebras. Journal of Algebraic Combinatorics, Tome 37 (2013) no. 1, pp. 87-116. http://geodesic.mathdoc.fr/item/JAC_2013__37_1_a3/