There is a nice tool in representation theory, the Howe duality, which as I know works for certain pairs of classical Lie algebras (the reference to the complete list of Howe dual pairs is appreciated very much). Is there any extension of the Howe duality for exceptional algebras?



Howe duality for exceptional algebras
There is a theory of dual reductive pairs and examples for exceptional Lie algebras.
For example, in $E\_8$ we have dual reductive pairs $(A\_1,E\_7)$, $(A\_2,E\_6)$, $(G\_2,F\_4)$, $(D\_4,D\_4)$. These are used implicitly in constructions of $E\_8$; for example $(G\_2,F\_4)$
corresponds to the Freudenthal-Tits construction and $(D\_4,D\_4)$ corresponds to the triality construction.


A reference is: 
MR1264015 (95b:17010) Rubenthaler, Hubert  

Les paires duales dans les algèbres de Lie réductives.
(French) [Dual pairs in reductive Lie algebras]  

Astérisque No. 219 (1994), 121 pp.


These seem to be of interest from the point of view of automorphic forms which I know nothing about.


