Invariant Differential Operators for Non-Compact Lie Groups: the Reduced SU(4,4) Multiplets

Abstract

In the present paper we continue the project of systematic construction of invariant differential operators on the example of the non-compact algebras $su(n,n)$. Earlier were given the main multiplets of indecomposable elementary representations for $n\le 4$, and the reduced ones for $n=2,3$. Here we give all reduced multiplets containing physically relevant representations including the minimal ones for $n=4$. Due to the recently established parabolic relations the results are valid also for the algebras $sl(8,\mathbb{R})$ and $s{u}^{\ast }(8)$ with suitably chosen maximal parabolic subalgebras.

35 pages, 21 figures, Lectures at "Third International School on Symmetry and Integrable Systems" and at "Humboldt Kolleg on Symmetry and Integrable Systems", Tsakhkadzor, Armenia, July 2013; V2: small correction. V3: changed normalization of conformal weight. arXiv admin note: substantial text overlap with arXiv:1312.5998

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