6 papers · 1 filter
An analogue of Whittaker reduction for group-valued moment maps
Ana Balibanu
We construct an analogue of Whittaker reduction for Poisson actions of a semisimple complex Poisson-Lie group G. The reduction takes place along a class of transversal slices to un…
Wonderful varieties with a view towards Poisson geometry
Ana Balibanu
These are expanded lecture notes from the author's minicourse at the 2022 Poisson Geometry Summer School, which took place at the Centre de Recerca Matematica in Barcelona, Spain.…
Steinberg slices and group-valued moment maps
Ana Balibanu
We define a class of transversal slices in spaces which are quasi-Poisson for the action of a complex semisimple group G. This is a multiplicative analogue of Whittaker reduction.…
Perverse sheaves and the cohomology of regular Hessenberg varieties
Ana Balibanu, Peter Crooks
We use the Springer correspondence to give a partial characterization of the irreducible representations which appear in the Tymoczko dot-action of the Weyl group on the cohomology…
The partial compactification of the universal centralizer
Ana Balibanu
The universal centralizer of a semisimple algebraic group is the family of centralizers of regular elements, parametrized by their conjugacy classes. When the group is of adjoint t…
The Peterson Variety and the Wonderful Compactification
Ana Balibanu
We look at the centralizer in a semisimple algebraic group of a regular nilpotent element, and show that its closure in the wonderful compactification is isomorphic to the Pete…