An O(2,n) formulation of invariant theory for elliptic Weyl group

TL;DR

This paper introduces a new formulation of invariant theory for elliptic Weyl groups using the group O(2,n), establishing a connection with Frobenius manifolds and conformal structures.

Contribution

It provides a novel O(2,n) formulation for elliptic Weyl group invariant theory and links it to Frobenius manifolds via a conformal Frobenius structure.

Findings

Defined a $ extbackslash C^*$-bundle as an elliptic Weyl group quotient

Established a conformal Frobenius structure on the bundle

Identified good sections with previously constructed Frobenius manifolds

Abstract

In this paper, we give a new formulation of invariant theory for elliptic Weyl group using the group O(2,n). As an elliptic Weyl group quotient, we define a suitable $\C^*$-bundle. We show that it has a conformal Frobenius structure which we define in this paper. Then its good section could be identified with a Frobenius manifold which we constructed in arXiv:math/0611553.