Classification of extremally irreducible and normally irreducible representations of semisimple complex connected Lie groups
Izvestiya. Mathematics , Tome 5 (1971) no. 3, pp. 589-613
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A new concept of “extremal irreducibility” for representations of Lie groups in separable locally convex spaces is introduced. All extremally irreducible representations of semisimple complex Lie groups are classified to within equivalence, i.e. to within topological isomorphism rearranging representation operators. Analogous results are obtained for other variants of axiomatics (normal irreducibility, Gel'fand irreducibility, complete irreducibility).
@article{IM2_1971_5_3_a5,
author = {D. P. Zhelobenko},
title = {Classification of extremally irreducible and normally irreducible representations of semisimple complex connected {Lie} groups},
journal = {Izvestiya. Mathematics },
pages = {589--613},
publisher = {mathdoc},
volume = {5},
number = {3},
year = {1971},
language = {en},
url = {http://geodesic.mathdoc.fr/item/IM2_1971_5_3_a5/}
}
TY - JOUR AU - D. P. Zhelobenko TI - Classification of extremally irreducible and normally irreducible representations of semisimple complex connected Lie groups JO - Izvestiya. Mathematics PY - 1971 SP - 589 EP - 613 VL - 5 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/IM2_1971_5_3_a5/ LA - en ID - IM2_1971_5_3_a5 ER -
%0 Journal Article %A D. P. Zhelobenko %T Classification of extremally irreducible and normally irreducible representations of semisimple complex connected Lie groups %J Izvestiya. Mathematics %D 1971 %P 589-613 %V 5 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/item/IM2_1971_5_3_a5/ %G en %F IM2_1971_5_3_a5
D. P. Zhelobenko. Classification of extremally irreducible and normally irreducible representations of semisimple complex connected Lie groups. Izvestiya. Mathematics , Tome 5 (1971) no. 3, pp. 589-613. http://geodesic.mathdoc.fr/item/IM2_1971_5_3_a5/