Quiver-graded Richardson orbits

And the Graded Kronecker Quiver

The topology of Lagrangian submanifolds gives rise to some of the most basic, and also most difficult, questions in symplectic geometry. We have many tools that can be brought to bear on these questions, but each one is effective only in a special class of situations, and their interrelation is by no means clear. The present paper is a piece of shamelessly biased propaganda for a relatively obs...

Richardson Orbits for Real Classical Groups

Some remarks on Richardson orbits in complex symmetric spaces

Roger W. Richardson proved that any parabolic subgroup of a complex semisimple Lie group admits an open dense orbit in the nilradical of its corresponding parabolic subalgebra. In the case of complex symmetric spaces we show that there exist some large classes of parabolic subgroups for which the analogous statement which fails in general, is true. Our main contribution is the extension of a th...

Rank Two Quiver Gauge Theory, Graded Connections and Noncommutative Vortices

We consider equivariant dimensional reduction of Yang-Mills theory on Kähler manifolds of the form M×CP 1×CP . This induces a rank two quiver gauge theory on M which can be formulated as a Yang-Mills theory of graded connections on M . The reduction of the Yang-Mills equations on M×CP 1×CP 1 induces quiver gauge theory equations on M and quiver vortex equations in the BPS sector. When M is the ...

Modelling Richardson Orbits for Son via ∆-filtered Modules

We study the ∆-filtered modules for the Auslander algebra of k[T ]/Tn ⋊C2 where C2 is the cyclic group of order two. The motivation for this is the bijection between parabolic orbits in the nilradical of a parabolic subgroup of SLn and certain ∆-filtered modules for the Auslander algebra of k[T ]/Tn as found by Hille and Röhrle and Brüstle et al., cf. [HR99] [BHRR99]. Under this bijection, the ...