Marek Gluza<p><span class="h-card"><a href="https://qubit-social.xyz/@markusheinrich" class="u-url mention" rel="nofollow noopener" target="_blank">@<span>markusheinrich</span></a></span> explained <a href="https://mathstodon.xyz/tags/math" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>math</span></a> to me in <a href="https://mathstodon.xyz/tags/benasque" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>benasque</span></a> how the twirl over a real adjoint representation instead of a complex one plays out in relation to <a href="https://mathstodon.xyz/tags/SchursLemma" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>SchursLemma</span></a>. The <a href="https://mathstodon.xyz/tags/commutatant" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>commutatant</span></a> needs to be a <a href="https://mathstodon.xyz/tags/divisionRing" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>divisionRing</span></a> and there's only one over the complex numbers, the complex numbers. Over real numbers there are two more possibilities, real numbers and quaternions. Something called the Frobenius indicator is a way to know what will be the <a href="https://mathstodon.xyz/tags/rank" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>rank</span></a> of the projector appearing in the result of the twirl for a given <a href="https://mathstodon.xyz/tags/irrep" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>irrep</span></a>.</p>