I found this notation $U^\boxplus$ in the paper 'Superpotentials for superconformal Chern-Simons theories from representation theory' by Paul de Medeiros, José Figueroa-O'Farrill and Elena Méndez-Escobar. Archive: https://arxiv.org/abs/0908.2125. They don't explain this notation while making a lot of effort explaining other notations they introduce, so I guess this one is fairly familiar within mathematical physics. However as a representation theorist I have never seen it before.
The context is the decompostion $\Lambda^2S^2U = \Lambda^4U \oplus U^\boxplus$ where $U$ is a (real) vector space, so it stands to reason that $\Lambda$ and $S$ denote exterior and symmetric powers respectively.
The vector space $U$ is a representation of a Lie algebra, but I do not know whether this plays any role in the definition of $U^\boxplus$.
Can anyone tell me what to make of this notation? Thanks in advance!