Automorphisms of groups and a higher rank JSJ decomposition I: RAAGs and a higher rank Makanin-Razborov diagram

Higher rank Einstein solvmanifolds

In this paper we study the structure of standard Einstein solvmanifolds of arbitrary rank. Also the validity of a variational method for finding standard Einstein solvmanifolds is proved.

GENERALIZED HIGHER-RANK NUMERICAL RANGE

In this note, a generalization of higher rank numerical range isintroduced and some of its properties are investigated

Rank Gradient and the Jsj Decomposition

GENERALIZED JOINT HIGHER-RANK NUMERICAL RANGE

The rank-k numerical range has a close connection to the construction of quantum error correction code for a noisy quantum channel. For noisy quantum channel, a quantum error correcting code of dimension k exists if and only if the associated joint rank-k numerical range is non-empty. In this paper the notion of joint rank-k numerical range is generalized and some statements of [2011, Generaliz...

Diagram Automorphisms and Rank-level Duality

We study the effect of diagram automorphisms on rank-level duality. We create new symplectic rank-level dualities from T. Abe’s symplectic rank-level duality on genus zero smooth curves with marked points and chosen coordinates. We also show that ranklevel dualities for the pair sl(r), sl(s) in genus 0 arising from representation theory can also be obtained from the parabolic strange dualities ...