Analogies for Compact Two-point Homogeneous Spaces

Abstract A definition of a convolution of tensor fields on group manifolds is given, which is then generalised to generic homogeneous spaces. This is applied to the product of gauge fields in the context of ‘gravity = gauge × gauge’. In particular, it is shown that the linear Becchi-Rouet-Stora-Tyutin (BRST) gauge transformations of two Yang-Mills gauge fields generate the linear BRST diffeomorphism transformations of the graviton. This facilitates the definition of the ‘gauge × gauge’ convolution product on, for example, the static Einstein universe, and more generally for ultrastatic spacetimes with compact spatial slices.

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Equivariant Filter (EqF): A General Filter Design for Systems on Homogeneous Spaces

2020 59th IEEE Conference on Decision and Control (CDC) ◽

10.1109/cdc42340.2020.9303813 ◽

2020 ◽

Author(s):

Pieter van Goor ◽

Tarek Hamel ◽

Robert Mahony

Keyword(s):

Homogeneous Spaces ◽

Filter Design

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LAURENT POLYNOMIAL LANDAU–GINZBURG MODELS FOR COMINUSCULE HOMOGENEOUS SPACES

Transformation Groups ◽

10.1007/s00031-020-09636-7 ◽

2021 ◽

Author(s):

PETER SPACEK

Keyword(s):

Homogeneous Space ◽

Homogeneous Spaces ◽

Laurent Polynomial ◽

Complete Intersections ◽

Laurent Polynomials ◽

Young Diagrams ◽

Similar Shape ◽

Algebraic Torus ◽

The One ◽

Polynomial Potentials

AbstractIn this article we construct Laurent polynomial Landau–Ginzburg models for cominuscule homogeneous spaces. These Laurent polynomial potentials are defined on a particular algebraic torus inside the Lie-theoretic mirror model constructed for arbitrary homogeneous spaces in [Rie08]. The Laurent polynomial takes a similar shape to the one given in [Giv96] for projective complete intersections, i.e., it is the sum of the toric coordinates plus a quantum term. We also give a general enumeration method for the summands in the quantum term of the potential in terms of the quiver introduced in [CMP08], associated to the Langlands dual homogeneous space. This enumeration method generalizes the use of Young diagrams for Grassmannians and Lagrangian Grassmannians and can be defined type-independently. The obtained Laurent polynomials coincide with the results obtained so far in [PRW16] and [PR13] for quadrics and Lagrangian Grassmannians. We also obtain new Laurent polynomial Landau–Ginzburg models for orthogonal Grassmannians, the Cayley plane and the Freudenthal variety.

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