Standard Representations of Simple Lie Algebras
1968 ◽
Vol 20
◽
pp. 344-361
◽
Keyword(s):
Let L be any simple finite-dimensional Lie algebra (defined over the field K of complex numbers). Cartan's theory of weights is used to define sets of (algebraic) representations of L that can be characterized in terms of left ideals of the universal enveloping algebra of L. These representations, called standard, generalize irreducible representations that possess a dominant weight. The newly obtained representations are all infinite-dimensional. Their study is initiated here by obtaining a partial solution to the problem of characterizing them by means of sequences of elements in K.
1965 ◽
Vol 25
◽
pp. 211-220
◽
2017 ◽
Vol 16
(03)
◽
pp. 1750053
◽
2009 ◽
Vol 20
(03)
◽
pp. 339-368
◽
1976 ◽
Vol 28
(1)
◽
pp. 174-180
◽
1990 ◽
Vol 05
(24)
◽
pp. 1967-1977
◽
Keyword(s):
2010 ◽
Vol 82
(3)
◽
pp. 401-423
Keyword(s):
2009 ◽
Vol 146
(2)
◽
pp. 351-378
◽
2001 ◽
Vol 53
(2)
◽
pp. 225-243
◽
Keyword(s):
Keyword(s):