# Geometry and Physics of Sp(3)/Sp(1)^3

@article{Eichinger2018GeometryAP, title={Geometry and Physics of Sp(3)/Sp(1)^3}, author={B. E. Eichinger}, journal={arXiv: General Physics}, year={2018} }

The action of $Sp(3)$ on a vector space $V_3\in \mathbb H^3$ is analyzed. The transitive action of the group is conveyed by the flag manifold (coset space) $Sp(3)/Sp(1)^3\sim G/H$, a Wallach space. The curvature two-forms are shown to mediate pair-wise interactions between the components of the $\mathbb H^3$ vector space. The root space of the flag manifold is shown to be isomorphic to that of $SU(3)$, suggesting similarities between the representations of the flag manifold and those of $SU(3…

## One Citation

### Canonical Quantum Coarse-Graining and Surfaces of Ignorance

- Computer Science
- 2021

A canonical quantum coarse-graining is introduced and negentropy is used to connect ignorance as measured by quantum information entropy and ignorance related to quantum coarsegraining.

## 16 References

### Projection from Yang-Mills Geometry to AdS Space

- Physics
- 2015

The geometry that yields the gauge potential and curvature form of Yang-Mills theory is known to be $Sp(2)/Sp(1)\times Sp(1)\sim S^4$. The projective metric for this space will be constructed and the…

### Bosons Live in Symplectic Coset Spaces

- Physics
- 2009

A theory for the transitive action of a group on the configuration space of a system of fermions is shown to lead to the conclusion that bosons can be represented by the action of cosets of the…

### Spin and the Symplectic Flag Manifold

- Mathematics
- 2011

A theory for the transitive action of a group on the conguration space of a system of particles is shown to lead to the conclusion that interactions can be represented by the action of cosets of the…

### Sigma models on flags

- ArtSciPost Physics
- 2019

The general flag model exhibits several new elements that are not present in the special case of the well-known jats:inline-formula, which depends on more parameters, its global symmetry can be larger, and its ’t Hooft anomalies can be more subtle.

### Representations of finite and compact groups

- Mathematics
- 1995

Groups and counting principles Fundamentals of group representations Abstract theory of representations of finite groups Representations of concrete finite groups. I: Abelian and Clifford groups…

### The theory of gauge fields in four dimensions

- Mathematics
- 1985

Introduction The geometry of connections The self-dual Yang-Mills equations The moduli space Fundamental results of K. Uhlenbeck The Taubes existence theorem Final arguments.

### Lie Groups and Compact Groups

- Mathematics
- 1977

1. Analytic manifolds 2. Lie groups and Lie algebras 3. The Campbell-Baker-Hausdorff formula 4. The geometry of Lie groups 5 Lie subgroups and subalgebras 6. Characterizations and structure of…

### Bull

- Amer. Math. Soc. 52, 1
- 1946

### Particle Data Group), Chin

- Phys. C,
- 2016