# 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} }

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.

## 5 Citations

### Singular polynomials from orbit spaces

- MathematicsCompositio Mathematica
- 2012

Abstract We consider the polynomial representation S(V*) of the rational Cherednik algebra Hc(W) associated to a finite Coxeter group W at constant parameter c. We show that for any degree d of W and…

### Frobenius structures, Coxeter discriminants, and supersymmetric mechanics

- Mathematics
- 2020

This thesis contains two directions both related to Frobenius manifolds.
In the first part we deal with the orbit space $M_W = V/W$ of a finite Coxeter group $W$ acting in its reflection…

### The Saito determinant for Coxeter discriminant strata

- Mathematics
- 2020

Let $W$ be a finite Coxeter group and $V$ its reflection representation. The orbit space $\mathcal{M}_W= V/W$ has the remarkable Saito flat metric defined as a Lie derivative of the $W$-invariant…

### Root systems and quotients of deformations of simple singularities

- MathematicsJournal of Algebra
- 2019

### V-systems, holonomy Lie algebras and logarithmic vector fields

- Mathematics
- 2014

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

- Mathematics
- 1993

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

- Mathematics, Physics
- 1993

### Invariants of Finite Groups Generated by Reflections

- Economics
- 1955

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

- Mathematics, Physics
- 1994

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

- Mathematics
- 1988

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

### Discrete Groups Generated by Reflections

- Mathematics
- 1934

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…