Izvestiya. Mathematics, Tome 8 (1974) no. 4, pp. 836-866
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A. N. Rudakov. Irreducible representations of infinite-dimensional Lie algebras of Cartan type. Izvestiya. Mathematics, Tome 8 (1974) no. 4, pp. 836-866. http://geodesic.mathdoc.fr/item/IM2_1974_8_4_a3/
@article{IM2_1974_8_4_a3,
author = {A. N. Rudakov},
title = {Irreducible representations of~infinite-dimensional {Lie} algebras of {Cartan} type},
journal = {Izvestiya. Mathematics},
pages = {836--866},
year = {1974},
volume = {8},
number = {4},
language = {en},
url = {http://geodesic.mathdoc.fr/item/IM2_1974_8_4_a3/}
}
TY - JOUR
AU - A. N. Rudakov
TI - Irreducible representations of infinite-dimensional Lie algebras of Cartan type
JO - Izvestiya. Mathematics
PY - 1974
SP - 836
EP - 866
VL - 8
IS - 4
UR - http://geodesic.mathdoc.fr/item/IM2_1974_8_4_a3/
LA - en
ID - IM2_1974_8_4_a3
ER -
%0 Journal Article
%A A. N. Rudakov
%T Irreducible representations of infinite-dimensional Lie algebras of Cartan type
%J Izvestiya. Mathematics
%D 1974
%P 836-866
%V 8
%N 4
%U http://geodesic.mathdoc.fr/item/IM2_1974_8_4_a3/
%G en
%F IM2_1974_8_4_a3
In this paper the irreducible representations of infinite-dimensional filtered Lie algebras are studied. The concept of the height of a representation is introduced, and it is proved that the representations of height greater than one of the Lie algebras $\mathbf W_n$, $\mathbf S_n$, $\mathbf H_n$ and $\mathbf K_n$ are induced. The representations of height one of the algebras $\mathbf W_n$ are also described.
