8 papers
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.…
Reduction along strong Dirac maps
Ana Balibanu, Maxence Mayrand
We develop a general procedure for reduction along strong Dirac maps, which are a broad generalization of Poisson momentum maps. We recover a large number of familiar constructions…
A quasi-Poisson structure on the multiplicative Grothendieck-Springer resolution
Ana Balibanu
In this note we show that the multiplicative Grothendieck-Springer space has a natural quasi-Poisson structure. The associated group-valued moment map is the resolution morphism, a…
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…