• Corpus ID: 115158120

Frobenius manifolds associated to Coxeter groups of type E_7 and E_8

@article{Abriani2009FrobeniusMA,
  title={Frobenius manifolds associated to Coxeter groups of type E\_7 and E\_8},
  author={Devis Abriani},
  journal={arXiv: Differential Geometry},
  year={2009}
}
  • Devis Abriani
  • Published 28 October 2009
  • Mathematics
  • arXiv: Differential Geometry
Flat coordinates for Frobenius manifolds defined on the orbit space of a Coxeter group W are specified through a certain system of generators of W-invariant polynomials. In this note, starting from basic invariants proposed by M.Mehta, we calculate flat coordinates for the exceptional groups of type E_7 and E_8, leading to a derivation of the potentials for the associated Frobenius structures. 

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It is shown that the description of certain class of representations of the holonomy Lie algebra associated to hyperplane arrangement $\Delta$ is essentially equivalent to the classification of

References

SHOWING 1-10 OF 12 REFERENCES

On a Linear Structure of the Quotient Variety by a Finite Reflexion Group

The objective of the article is to show that the orbit space of a finite reflection group acting on the complexification of the real vector space carries naturally a complex vector space structure Q

Graph rings and integrable perturbations of N=2 superconformal theories

Invariants of Finite Groups Generated by Reflections

JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and

Geometry of 2D topological field theories

These lecture notes are devoted to the theory of “equations of associativity” describing geometry of moduli spaces of 2D topological field theories.

Basic sets of invariant polynomials for finite reflection groups

A basic net of invariant polynomials is explicitly given for each non-factorizable finite reflection group.

Discrete Groups Generated by Reflections

1-3. Polytopes with restricted dihedral angles 590 4-7. Fundamental regions 594 8. The abstract definition 599 9. Complete enumeration of the irreducible groups 601 10-13. Continued products of the