Explicit SL_2(C)-module decompositions and Jordan forms are given for the image of regular unipotents under any irreducible polynomial representation of GL_3(C).
Character theory at a torsion element, 2025, 2504.14684 http://arxiv.org/abs/2504.14684
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Image of Regular Unipotent under a Representation of $\mathrm{GL}_3(\mathbb{C})$
Explicit SL_2(C)-module decompositions and Jordan forms are given for the image of regular unipotents under any irreducible polynomial representation of GL_3(C).