Irreducible representations of simple Lie algebras by differential operators
Keyword(s):
AbstractWe describe a systematic method to construct arbitrary highest-weight modules, including arbitrary finite-dimensional representations, for any finite dimensional simple Lie algebra $${\mathfrak {g}}$$ g . The Lie algebra generators are represented as first order differential operators in $$\frac{1}{2} \left( \dim {\mathfrak {g}} - \text {rank} \, {\mathfrak {g}}\right) $$ 1 2 dim g - rank g variables. All rising generators $$\mathbf{e}$$ e are universal in the sense that they do not depend on representation, the weights enter (in a very simple way) only in the expressions for the lowering operators $$\mathbf{f}$$ f . We present explicit formulas of this kind for the simple root generators of all classical Lie algebras.
1995 ◽
Vol 52
(2)
◽
pp. 285-302
◽
Keyword(s):
1968 ◽
Vol 20
◽
pp. 344-361
◽
1965 ◽
Vol 25
◽
pp. 211-220
◽
2017 ◽
Vol 153
(4)
◽
pp. 678-716
◽
1971 ◽
Vol 14
(1)
◽
pp. 113-115
◽
2007 ◽
Vol 5
◽
pp. 195-200
2016 ◽
Vol 2016
(716)
◽
Keyword(s):
2007 ◽
Vol 17
(03)
◽
pp. 527-555
◽