Michael Entov, Leonid Polterovich
Published 2009-06-26, updated 2009-09-01Version 2
Lie quasi-states on a real Lie algebra are functionals which are linear on any abelian subalgebra. We show that on the symplectic Lie algebra of rank at least 3 there is only one continuous non-linear Lie quasi-state (up to a scalar factor, modulo linear functionals). It is related to the asymptotic Maslov index of paths of symplectic matrices.
Comments: Minor corrections
On total Springer representations for the symplectic Lie algebra in characteristic 2 and the exotic case
A Whittaker category for the Symplectic Lie algebra
Two permanents in the universal enveloping algebras of the symplectic Lie algebras
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