Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Good Basic Invariants for Elliptic Weyl Groups and Frobenius Structures

Ikuo Satake

Abstract

In this paper, we define a set of good basic invariants for the elliptic Weyl group for the elliptic root system. For an elliptic root system of codimension $1$, we show that a set of good basic invariants gives a set of flat invariants obtained by Saito and Taylor coefficients of the good basic invariants give the structure constants of the multiplication of the Frobenius structure obtained by the author.

Good Basic Invariants for Elliptic Weyl Groups and Frobenius Structures

Abstract

In this paper, we define a set of good basic invariants for the elliptic Weyl group for the elliptic root system. For an elliptic root system of codimension , we show that a set of good basic invariants gives a set of flat invariants obtained by Saito and Taylor coefficients of the good basic invariants give the structure constants of the multiplication of the Frobenius structure obtained by the author.

Paper Structure

This paper contains 34 sections, 35 theorems, 147 equations.

Table of Contents

  1. Introduction
  2. Aim and results of the paper
  3. Acknowledgements
  4. $W$-invariants for elliptic root systems
  5. Elliptic root systems
  6. Hyperbolic extension
  7. Elliptic Weyl group
  8. Domains and Euler field
  9. The algebra of the invariants for the elliptic Weyl group
  10. Decomposition of the space $Y$
  11. Graded algebra
  12. Admissible triplet
  13. Graded algebra Isomorphism $\psi$
  14. The morphism $\varphi[g,\zeta,L]$
  15. The morphism $\psi[g,\zeta,L]$
  16. ...and 19 more sections

Key Result

Theorem 2.2

The $F({H})$-algebra $S^W$ is generated by a set of algebraically independent homogeneous generators $x^1,\cdots,x^{n}$$(n=l+1)$ with degrees $0 <d_1 \leq d_2 \cdots \leq d_n$ which we call a set of basic invariants.

Theorems & Definitions (70)

  • Definition 2.1
  • Theorem 2.2: Chevalley3Chevalley4Chevalley6Chevalley7Chevalley8Chevalley2Chevalley1Chevalley5
  • Definition 3.1
  • Definition 3.2
  • Proposition 3.3
  • Proof
  • Proposition 3.4
  • Proof
  • Proposition 3.5
  • Proof
  • ...and 60 more