5 papers
On the variety of Lagrangian subalgebras, II
Sam Evens, Jiang-Hua Lu
When is a complex semisimple Lie algebra, we study the variety of subalgebras of that are maximally isotropic with respect to…
Thompson's conjecture for real semi-simple Lie groups
Jiang-Hua Lu, Sam Evens
A proof of Thompson's conjecture for real semi-simple Lie groups has been given by Kapovich, Millson, and Leeb. In this note, we give another proof of the conjecture by using a the…
Representations of quantum tori and double-affine Hecke algebras
Vladimir Baranovsky, Sam Evens, Victor Ginzburg
We study a BGG-type category of infinite dimensional representations of H[W], a semi-direct product of the quantum torus with parameter `q' built on the root lattice of a semisimpl…
On the variety of Lagrangian subalgebras
Sam Evens, Jiang-Hua Lu
We study Lagrangian subalgebras of a semisimple Lie algebra with respect to the imaginary part of the Killing form. We show that the variety $\Lagr$ of Lagrangian subalgebras carri…
Poisson harmonic forms, Kostant harmonic forms, and the -equivariant cohomology of
Sam Evens, Jiang-Hua Lu
We characterize the harmonic forms on a flag manifold defined by Kostant in 1963 in terms of a Poisson structure. Namely, they are ``Poisson harmonic" with respect to the so-…