Sp(2n)(F-q(2))-invariants in irreducible unipotent representations of Sp Sp(4n)(F-q)

作者：Zhang Lei^*

来源：Journal of Algebra, 2013, 395: 24-46.

DOI：10.1016/j.jalgebra.2013.08.006

• Finite groups of Lie type
• Unipotent representations
• Distinguished representations
• Symmetric subgroups

We show that for any irreducible representation of Sp(4n)(F-q), the subspace of all its Sp(2)(n)(F-q(2))-invariants is at most onedimensional. In terms of Lusztig symbols, we give a complete list of irreducible unipotent representations of Sp(4n)(F-q) which have a non-zero SSp(2)(n)(F-q(2))-invariant and, in particular, we prove that every irreducible unipotent cuspidal representation has a onedimensional subspace of Sp(2)(n)(F-q(2))-invariants. As an application, we give an elementary proof of the fact that the unipotent cuspidal representation is defined over Q, which was proved by Lusztig in [12].

• 出版日期2013-12-1