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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 real form of the exceptional Lie algebra \(F_4\) . We consider induction from a maximal parabolic algebra containing the algebra  sp(3). 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.

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Quaternionic Discrete Series and Invariant Differential Operators over the Lie Algebra \(F'_4\)

  • 会议论文

  • 发表日期：

    2025年

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  • V. K. Dobrev

摘要

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 real form of the exceptional Lie algebra \(F_4\) . We consider induction from a maximal parabolic algebra containing the algebra  sp(3). 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.