23 citations · 78 across the 23 of their papers we have counts for
14 papers · 1 filter
Orbits on a product of two flags and a line and the Bruhat order, II
Mark Colarusso, Sam Evens
Let be the complex general linear group and let $\B_{n}$ be its flag variety. A Borel subgroup of acts on $\B_{n}\times \mathbb{P}^{n-1}$ diagonally w…
Orbits on a product of two flags and a line and the Bruhat Order, I
Mark Colarusso, Sam Evens
Let be the complex general linear group and let be its flag variety. The standard Borel subgroup of upper triangular matrices acts on th…
Wonderful Compactification of a Cartan Subalgebra of a Semisimple Lie Algebra
Sam Evens, Yu Li
Let be a Cartan subalgebra of a complex semisimple Lie algebra We define a compactification of , which is analogous t…
-orbits on the flag variety and the Bruhat graph of the symmetric group
Mark Colarusso, Sam Evens
Let be the complex general linear group and embed in the top left hand corner of . The standard Borel subgroup of upper triangular…
B_{n-1}-bundles on the flag variety, II
Mark Colarusso, Sam Evens
This paper is the sequel to ``-bundles on the flag variety, I". We continue our study of the orbits of a Borel subgroup of (resp. ) ac…
B_{n-1}-bundles on the flag variety, I
Mark Colarusso, Sam Evens
We show that each orbit of a Borel subgroup of GL(n-1) (respectively SO(n-1)) on the flag variety of GL(n) (respectively of SO(n)) is a bundle over a -orbit on a…
Abelian Ideals and the Variety of Lagrangian Subalgebras
Sam Evens, Yu Li
For a semisimple algebraic group of adjoint type with Lie algebra over the complex numbers, we establish a bijection between the set of closed orbits of the group…
The Complex Orthogonal Gelfand-Zeitlin System
Mark Colarusso, Sam Evens
In this paper, we use the theory of algebraic groups to prove a number of new and fundamental results about the orthogonal Gelfand-Zeitlin system. We show that the moment map (orth…
Eigenvalue Coincidences and Multiplicity Free Spherical Pairs
Mark Colarusso, Sam Evens
In recent work, we related the structure of subvarieties of complex matrices defined by eigenvalue coincidences to -orbits on the flag variety of $\…
The relative Hochschild-Serre spectral sequence and the Belkale-Kumar product
Sam Evens, William Graham
We consider the Belkale-Kumar cup product on for a generalized flag variety with parameter $t \in \C^m$, where . For each $t\in \C^m$,…
The Gelfand-Zeitlin integrable system and K-orbits on the flag variety
Mark Colarusso, Sam Evens
In this expository paper, we provide an overview of the Gelfand-Zeiltin integrable system on the Lie algebra of complex matrices $\fgl(n,\C)$ introduced by Kostant and…
K-orbits on the flag variety and strongly regular nilpotent matrices
Mark Colarusso, Sam Evens
In two 2006 papers, Kostant and Wallach constructed a complexified Gelfand-Zeitlin integrable system for the Lie algebra $\fgl(n+1,\C)$ and introduced the strongly regular elements…
On some invariants of orbits in the flag variety under a symmetric subgroup
Sam Evens, Jiang-Hua Lu
Let be a connected reductive algebraic group over an algebraically closed field of characteristic not equal to 2, let $\B$ be the variety of all Borel subgroups of $G…
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…