Compatible intertwiners for representations of finite nilpotent groups

Details Compatible intertwiners for representations of finite nilpotent groups Compatible intertwiners for representations of finite nilpotent groups

2009-09-30

arxiv.org/abs/0909.5670v2

Represent. Theory 15 (2011), 407-432

Mathematics

Representation Theory

Scientific paper

We sharpen the orbit method for finite groups of small nilpotence class by associating representations to functionals on the corresponding Lie rings. This amounts to describing compatible intertwiners between representations parameterized by an additional choice of polarization. Our construction is motivated by the theory of the linearized Weil representation of the symplectic group. In particular, we provide generalizations of the Maslov index and the determinant functor to the context of finite abelian groups.

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