The adjoint representation of a reductive group and hyperplane arrangements

The Adjoint Representation of a Reductive Group and Hyperplane Arrangements

Let G be a connected reductive algebraic group with Lie algebra g defined over an algebraically closed field, k, with char k = 0. Fix a parabolic subgroup of G with Levi decomposition P = LU where U is the unipotent radical of P . Let u = Lie(U) and let z denote the center of Lie(L). Let T be a maximal torus in L with Lie algebra t. Then the root system of (g, t) is a subset of t∗ and by restri...

heterogeneity within the orientalist discourse: representation of the orient in womens travelogues and mens paintings

from 1950s onward, new theories and critical approaches burgeoned across humanities. these theories were context-oriented; as a result, the analysis of discursive practices gained significance. thus, social, political, historical and cultural discourses that have been hitherto marginalized and considered inferior to literary texts, were introduced as important texts to be analyzed by critics. o...

The Topology of Hyperplane Arrangements

Random Walk and Hyperplane Arrangements

Let C be the set of chambers of a real hyperplane arrangement. We study a random walk on C introduced by Bidigare, Hanlon, and Rockmore. This includes various shuuing schemes used in computer science, biology, and card games. It also includes random walks on zonotopes and zonotopal tilings. We nd the stationary distributions of these Markov chains, give good bounds on the rate of convergence to...

Branched Polymers and Hyperplane Arrangements

We generalize the construction of connected branched polymers and the notion of the volume of the space of connected branched polymers studied by Brydges and Imbrie [BI], and Kenyon and Winkler [KW] to any hyperplane arrangement A. The volume of the resulting configuration space of connected branched polymers associated to the hyperplane arrangement A is expressed through the value of the chara...