A System of Third-Order Differential Operators Conformally Invariant under $\mathfrak{sl}(3,\mathbb{C})$ and $\mathfrak{so}(8,\mathbb{C})$

Toshihisa Kubo

A System of Third-Order Differential Operators Conformally Invariant under $\mathfrak{sl}(3,\mathbb{C})$ and $\mathfrak{so}(8,\mathbb{C})$

Representation Theory 2012-09-11 v1

Authors: Toshihisa Kubo

Abstract

In earlier work, Barchini, Kable, and Zierau constructed a number of conformally invariant systems of differential operators associated to Heisenberg parabolic subalgebras in simple Lie algebras. The construction was systematic, but the existence of such a system was left open in two cases, namely, the $\Omega_3$ system for type $A_2$ and type $D_4$ . Here, such a system is shown to exist for both cases. The construction of the system may also be interpreted as giving an explicit homomorphism between generalized Verma modules.

Keywords

conformally invariant differential operators Heisenberg parabolic subalgebras simple Lie algebras generalized Verma modules Lie algebra representations

Cite

@article{arxiv.1104.1999,
  title  = {A System of Third-Order Differential Operators Conformally Invariant under $\mathfrak{sl}(3,\mathbb{C})$ and $\mathfrak{so}(8,\mathbb{C})$},
  author = {Toshihisa Kubo},
  journal= {arXiv preprint arXiv:1104.1999},
  year   = {2012}
}

Comments

This paper contains the results in the previous paper for type D_4 as well

A System of Third-Order Differential Operators Conformally Invariant under $\mathfrak{sl}(3,\mathbb{C})$ and $\mathfrak{so}(8,\mathbb{C})$

Abstract

Keywords

Cite

Comments

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