Time optimal factorizations on compact Lie groups

Factorizations in the Irreducible Characters of Compact Semisimple Lie Groups

Our goal is to describe factorizations of the characters of irreducible representations of compact semisimple Lie groups. It is well-known that for a given Lie group G of rank n, the Virtual Representation Ring R(G) with the operations of tensor product, direct sum, and direct difference is isomorphic to a polynomial ring with integer coefficients and number of generators equal to n. As such, R...

Probability on Compact Lie Groups

Spin Dynamics: A Paradigm for Time Optimal Control on Compact Lie Groups

The development of efficient time optimal control strategies for coupled spin systems plays a fundamental role in nuclear magnetic resonance (NMR) spectroscopy. In particular, one of the major challenges lies in steering a given spin system to a maximum of its so-called transfer function. In this paper we study in detail these questions for a system of two weakly coupled spin-12 particles. Firs...

Compact Lie Groups

The first half of the paper presents the basic definitions and results necessary for investigating Lie groups. The primary examples come from the matrix groups. The second half deals with representation theory of groups, particularly compact groups. The end result is the Peter-Weyl theorem.

Towards coordination algorithms on compact Lie groups

The present work considers the design of control algorithms to coordinate a swarm of identical, autonomous, cooperating agents that evolve on compact Lie groups. The objective is that the agents reach a so-called consensus state without using any external reference. In the same line of thought, a leader-follower approach where ’follower’ agents would track one ’leader’ agent is excluded, in fav...