Equivariant D-modules on 2 × 2 × 2 hypermatrices

Notes on Equivariant D-modules

Interactive Visualization of 2-D Persistence Modules

The goal of this work is to extend the standard persistent homology pipeline for exploratory data analysis to the 2-D persistence setting, in a practical, computationally efficient way. To this end, we introduce RIVET, a software tool for the visualization of 2-D persistence modules, and present mathematical foundations for this tool. RIVET provides an interactive visualization of the barcodes ...

Using 2×2 switching modules to build large 2-D MEMS optical switches

MEMS optical switch technology is one of the key technologies in Wavelength Division Multiplexing (WDM) optical networks. Although the 2-D MEMS optical switch technology is mature, the commonly used crossbar architecture is not amenable to building large switches. In this paper, we propose a design of 2 × 2 switching modules, and use it to build large 2-D MEMS optical switches with architecture...

2 Equivariant vector bundles on group completions

We describe the category of equivariant vector bundles on a smooth (partial) group completion of an adjoint simple algebraic group. As a corollary of our description, we prove that every equivariant vector bundle of rank less than or equal to rkG on the canonical (wonderful) completion splits into a direct sum of line bundles.

2 00 2 Reflection Equation , Twist , and Equivariant Quantization

We prove that the reflection equation (RE) algebra LR associated with a finite dimensional representation of a quasitriangular Hopf algebra H is twist-equivalent to the corresponding Faddeev-Reshetikhin-Takhtajan (FRT) algebra. We show that LR is a module algebra over the twisted tensor squareH R ⊗H and the double D(H). We define FRTand RE-type algebras and apply them to the problem of equivari...