I'm working through Introduction to Lie Algebras and Representation Theory by Humphreys, and I came across this notation $L.v$ as you can see in the picture. I cannot find where it's first introduced, or maybe it's assumed known.

Please help me, it's difficult to continue without knowing what this means.

  • 2
    $\begingroup$ The elements of $L$ are matrices, if you want. So $L.v=\{Av\mid A\in L\}$. $\endgroup$ – Dietrich Burde Jan 15 '18 at 19:17
  • $\begingroup$ @DietrichBurde Thank you! Now I can stop tearing my hair and read on. $\endgroup$ – Auclair Jan 15 '18 at 19:27

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