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  1. The notation $V\odot V$ means the symmetric tensor product$^1$ similar to that $V\wedge V$ means the antisymmetric tensor product.

  2. This can be generalized to higher tensor powers. e.g. ${\rm Sym}^3V~\equiv~ V\odot V\odot V~\equiv~V^{\odot 3},$ and $ \bigwedge{}^3V~\equiv~ V\wedge V\wedge V,$ and so forth.

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$^1$ The tensor product $V\otimes V$ is neither symmetric nor antisymmetric.

Qmechanic
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  • I believe, although I am not certain, that this answers my question... The dot-within-a-circle is the symmetric tensor product, and the upside-down V, or lambda, is the antisymmetric tensor product... Thank you!! It's just that, on the, Why isn't there a second baryon octet page, the capital-lambda looked normal, while the dot-circle looked like an exponent of some sort... – Kurt Hikes Jan 13 '21 at 14:03
  • I updated the answer. – Qmechanic Jan 13 '21 at 14:24
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    @KurtHikes As a note, the upside-down V is usually referred to as wedge, which is reflected in the LaTeX/MathJax command \wedge $\rightarrow \wedge$. – J. Murray Jan 13 '21 at 14:59