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Invariant Differential Operators for the Real Exceptional Lie Algebra $F"_4$

V. K. Dobrev

Abstract

In the present paper we continue the project of systematic construction of invariant differential operators on the example of the non-compact exceptional Lie algebra $F"_4$ which is the split rank one form of the exceptional Lie algebra $F_4$. We classify the reducible Verma modules over $F_4$ which are compatible with this induction. Thus, we obtain the classification of the corresponding invariant differential operators.

Invariant Differential Operators for the Real Exceptional Lie Algebra $F"_4$

Abstract

In the present paper we continue the project of systematic construction of invariant differential operators on the example of the non-compact exceptional Lie algebra which is the split rank one form of the exceptional Lie algebra . We classify the reducible Verma modules over which are compatible with this induction. Thus, we obtain the classification of the corresponding invariant differential operators.

Paper Structure

This paper contains 11 sections, 50 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Lie algebra
  4. Verma modules
  5. Structure theory of the real form
  6. Elementary representations
  7. Main multiplets of $F"_4$
  8. Reduced multiplets
  9. Main reduced multiplets
  10. Further reduced multiplets
  11. Concluding remarks

Figures (1)

  • Figure :