Geodesic
Complex Groups and Root Subgroup Factorization
Journal of Lie theory, Tome 28 (2018) no. 4, pp. 1095-1118
Cet article a éte moissonné depuis la source Heldermann Verlag

Voir la notice de l'article

Root subgroup factorization is a refinement of triangular (or LDU) factorization. For a complex reductive Lie group, and a choice of reduced factorization of the longest Weyl group element, the forward map from root subgroup coordinates to triangular coordinates is polynomial. We show that the forward map is injective on its set of regular points and that the inverse is rational. There is an algorithm for the inverse (involving LDU factorization), and a related explicit formula for Haar measure in root subgroup coordinates. In classical cases there are preferred reduced factorizations of the longest Weyl group elements, and conjecturally in these cases there are closed form expressions for root subgroup coordinates.
Classification : 22E67
Mots-clés : Complex reductive group, triangular factorization, root subgroup factorization 
@article{JLT_2018_28_4_JLT_2018_28_4_a8,
     author = {D. Pickrell},
     title = {Complex {Groups} and {Root} {Subgroup} {Factorization}},
     journal = {Journal of Lie theory},
     pages = {1095--1118},
     year = {2018},
     volume = {28},
     number = {4},
     url = {http://geodesic.mathdoc.fr/item/JLT_2018_28_4_JLT_2018_28_4_a8/}
}
TY  - JOUR
AU  - D. Pickrell
TI  - Complex Groups and Root Subgroup Factorization
JO  - Journal of Lie theory
PY  - 2018
SP  - 1095
EP  - 1118
VL  - 28
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/JLT_2018_28_4_JLT_2018_28_4_a8/
ID  - JLT_2018_28_4_JLT_2018_28_4_a8
ER  - 
%0 Journal Article
%A D. Pickrell
%T Complex Groups and Root Subgroup Factorization
%J Journal of Lie theory
%D 2018
%P 1095-1118
%V 28
%N 4
%U http://geodesic.mathdoc.fr/item/JLT_2018_28_4_JLT_2018_28_4_a8/
%F JLT_2018_28_4_JLT_2018_28_4_a8
D. Pickrell. Complex Groups and Root Subgroup Factorization. Journal of Lie theory, Tome 28 (2018) no. 4, pp. 1095-1118. http://geodesic.mathdoc.fr/item/JLT_2018_28_4_JLT_2018_28_4_a8/