so₆ℂ, so₇ℂ and so_mℂ

Abstract

This lecture is analogous in content (and prerequisites) to Lecture 17: we do some more low-dimensional examples and then describe the general picture of the representations of the orthogonal Lie algebras. One difference is that only half the irreducible representations of$\mathfrak{s}{\mathfrak{d}_m}\mathbb{C}$lie in the tensor algebra of the standard; to complete the picture of the representation theory we have to construct the spin representations, which is the subject matter of the following lecture. The first four sections are completely elementary (except possibly for the discussion of the isomorphism $\mathfrak{s}{{\mathfrak{o}}_{6}}\mathbb{C} \cong \mathfrak{s}{{\mathfrak{l}}_{4}}\mathbb{C}$ in §19.1); the last section assumes a knowledge of Lecture 6 and §15.3, but can be skipped by those who did not read those sections.