scholarly journals On the cohomology ring of some homogeneous spaces.

1975 ◽  
Vol 15 (1) ◽  
pp. 185-199 ◽  
Author(s):  
Hirosi Toda
Keyword(s):  
Homogeneous Spaces ◽  
Cohomology Ring

scholarly journals Affine symmetries of the equivariant quantum cohomology ring of rational homogeneous spaces

2009 ◽  
Vol 16 (1) ◽  
pp. 7-21 ◽  
Author(s):  
Pierre-Emmanuel Chaput ◽  
Laurent Manivel ◽  
Nicolas Perrin
Keyword(s):  
Homogeneous Spaces ◽  
Cohomology Ring ◽  
Quantum Cohomology

scholarly journals Quantum Cohomology of Minuscule Homogeneous Spaces III Semi-Simplicity and Consequences

2010 ◽  
Vol 62 (6) ◽  
pp. 1246-1263 ◽  
Author(s):  
P. E. Chaput ◽  
L. Manivel ◽  
N. Perrin
Keyword(s):  
Homogeneous Space ◽  
Homogeneous Spaces ◽  
Cohomology Ring ◽  
Quantum Cohomology ◽  
Previous Article ◽  
Complex Conjugation ◽  
Quantum Parameter ◽  
Strange Duality

AbstractWe prove that the quantum cohomology ring of any minuscule or cominuscule homogeneous space, specialized at q = 1, is semisimple. This implies that complex conjugation defines an algebra automorphism of the quantum cohomology ring localized at the quantum parameter. We check that this involution coincides with the strange duality defined in our previous article. We deduce Vafa–Intriligator type formulas for the Gromov–Witten invariants.

scholarly journals Combinatorial integers(m,nj)and Schubert calculus in the integral cohomology ring of infinite smooth flag manifolds

2006 ◽  
Vol 2006 ◽  
pp. 1-55
Author(s):  
Cenap Özel ◽  
Erol Yilmaz
Keyword(s):  
Homogeneous Spaces ◽  
Cohomology Ring ◽  
Schubert Calculus ◽  
Flag Manifolds ◽  
Cohomology Algebra ◽  
Loop Groups ◽  
Local Coefficient ◽  
Integral Cohomology ◽  
Ring Structures ◽  
Coefficient Ring

We discuss the calculation of integral cohomology ring ofLG/TandΩG. First we describe the root system and Weyl group ofLG, then we give some homotopy equivalences on the loop groups and homogeneous spaces, and calculate the cohomology ring structures ofLG/TandΩGfor affine groupA^2. We introduce combinatorial integers(m,nj)which play a crucial role in our calculations and give some interesting identities among these integers. Last we calculate generators for ideals and rank of each module of graded integral cohomology algebra in the local coefficient ringℤ[1/2].

scholarly journals Gauge × gauge = gravity on homogeneous spaces using tensor convolutions

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
L. Borsten ◽  
I. Jubb ◽  
V. Makwana ◽  
S. Nagy
Keyword(s):  
Homogeneous Spaces ◽  
Gauge Fields ◽  
Convolution Product ◽  
Tensor Fields ◽  
Einstein Universe ◽  
Gauge Transformations ◽  
Yang Mills ◽  
Static Einstein Universe ◽  
Definition Of ◽  
Gauge Gravity

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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