Sabine J. Lang

My research consists of different projects in the Theta correspondence. I work on restriction of the oscillator representation to dual pairs of type I, and I established a condition on the sizes of the subgroups to get a projective (g, K)-modules. I study real exceptional groups containing a pair with a group of type A2, in the spherical case. Similarly, I look at the non-spherical case when the pair contains a group of type G2.

The Theta correspondence can also be extended to complex groups. In exceptional groups, I study pairs with one member of typer G2. I also work with pairs arising naturally from the extended Dynkin diagram of simple Lie algebra, to get branching rules for the K-types of the minimal representation.

• Research Statement.

• Projective cases for the restriction of the oscillator representation to dual pairs of type I.   Preprint. arXiv:1711.10562 [math.RT] Submitted to The Pacific Journal of Mathematics.
• Poster on this paper.

• Restricting irreducible representations of Lie algebras to semisimple subalgebras.
• Poster.