Geodesic
Invariants of the Cox rings of low-complexity double flag varieties for classical groups
Trudy Moskovskogo matematičeskogo obŝestva, Trudy Moskovskogo Matematicheskogo Obshchestva, Tome 76 (2015) no. 1, pp. 85-150

Voir la notice de l'article provenant de la source Math-Net.Ru

We find the algebras of unipotent invariants of Cox rings for all double flag varieties of complexity 0 and 1 for the classical groups; namely, we obtain presentations of these algebras. It is well known that such an algebra is simple in the case of complexity 0. We show that, in the case of complexity 1, the algebra in question is either a free algebra or a hypersurface. Knowing the structure of this algebra permits one to effectively decompose tensor products of irreducible representations into direct sums of irreducible representations. 
@article{MMO_2015_76_1_a2,
     author = {E. V. Ponomareva},
     title = {Invariants of the {Cox} rings of low-complexity double flag varieties for classical groups},
     journal = {Trudy Moskovskogo matemati\v{c}eskogo ob\^{s}estva},
     pages = {85--150},
     publisher = {mathdoc},
     volume = {76},
     number = {1},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MMO_2015_76_1_a2/}
}
TY  - JOUR
AU  - E. V. Ponomareva
TI  - Invariants of the Cox rings of low-complexity double flag varieties for classical groups
JO  - Trudy Moskovskogo matematičeskogo obŝestva
PY  - 2015
SP  - 85
EP  - 150
VL  - 76
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MMO_2015_76_1_a2/
LA  - ru
ID  - MMO_2015_76_1_a2
ER  - 
%0 Journal Article
%A E. V. Ponomareva
%T Invariants of the Cox rings of low-complexity double flag varieties for classical groups
%J Trudy Moskovskogo matematičeskogo obŝestva
%D 2015
%P 85-150
%V 76
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MMO_2015_76_1_a2/
%G ru
%F MMO_2015_76_1_a2
E. V. Ponomareva. Invariants of the Cox rings of low-complexity double flag varieties for classical groups. Trudy Moskovskogo matematičeskogo obŝestva, Trudy Moskovskogo Matematicheskogo Obshchestva, Tome 76 (2015) no. 1, pp. 85-150. http://geodesic.mathdoc.fr/item/MMO_2015_76_1_a2/