200 citations · 1.6k across the 65 of their papers we have counts for
7 papers · 1 filter
Action-angle coordinates on coadjoint orbits and multiplicity free spaces from partial tropicalization
Anton Alekseev, Benjamin Hoffman, Jeremy Lane +1
Coadjoint orbits and multiplicity free spaces of compact Lie groups are important examples of symplectic manifolds with Hamiltonian groups actions. Constructing action-angle variab…
Concentration of symplectic volumes on Poisson homogeneous spaces
Anton Alekseev, Benjamin Hoffman, Jeremy Lane +1
For a compact Poisson-Lie group , the homogeneous space carries a family of symplectic forms , where is in the positive Weyl chamber and $s…
The Gelfand-Zeitlin system as a tropical limit of Ginzburg-Weinstein diffeomorphisms
Anton Alekseev, Jeremy Lane, Yanpeng Li
We show that the Ginzburg-Weinstein diffeomorphism of Alekseev-Meinrenken admits a scaling tropical limit on an open dense subset of $\mathfrak{u}(n)…
Inequalities from Poisson brackets
Anton Alekseev, Irina Davydenkova
We introduce the notion of tropicalization for Poisson structures on with coefficients in Laurent polynomials. To such a Poisson structure we associate a polyhedral…
A symplectic proof of the Horn inequalities
Anton Alekseev, Masha Podkopaeva, Andras Szenes
In this paper, we give a symplectic proof of the Horn inequalities on eigenvalues of a sum of two Hermitian matrices with given spectra. Our method is a combination of tropical cal…
Formulas of Verlinde type for non-simply connected groups
Anton Alekseev, Eckhard Meinrenken, Chris Woodward
We derive Verlinde's formula from the fixed point formula for loop groups proved in the companion paper "A fixed point formula for loop group actions", and extend it to compact, co…
A fixed point formula for loop group actions
Anton Alekseev, Eckhard Meinrenken, Chris Woodward
We express the index of the Dirac operator on symplectic quotients of a Hamiltonian loop group manifold with proper moment map in terms of fixed point data.