Introduction to Mathematical Logic, Sixth Edition
《Introduction to Mathematical Logic, Sixth Edition》 · 第 315 页 · Chapter 6，Section 6.2.2「Spin Representations」，Proposition 6.2.4
We call $\pi$ the spin representation of $\mathfrak{so}(V,\beta)$. The representation space has dimension $2^l$ when $\dim V = 2l+1$. Proposition 6.2.4. ($\dim V = 2l+1$) The spin representation of $\mathfrak{so}(V,\beta)$ is irreducible and has highest weight $\varpi_l = (\varepsilon_1 + \dots + \varepsilon_{l-1} + \varepsilon_l)/2$.