| Dual pair in a Lie algebra g is a pair of subalgebras g1 x g2 such that Zg ( gi ) = gj . The restriction of a representation pi of g is a sum of representations of g1 x g2 . It gives a correspondence of representations of g1 and g2 .; In the first part of this thesis we describe real forms of dual pairs gC2 x h in g of type En.; In the second part, we give a new construction of an ( eC6 , SL(3, C ) x SL(3, C ) x SL(3, C ))-modules annihilated by the Joseph ideal. Using this construction, we construct a correspondence between PGL(3, C )-modules and ( gC2 , SL(3, C ))-modules.; In the last part, we sketch a classification of ( gC2 , SL(3, C ))-modules which is needed in the second part. We give a classification of SL(3, C )-orbits on G2/B. This is the main ingredient for the classification of ( gC2 , SL(3, C ))-modules. |
