Groups and Manifolds by Pietro Giuseppe Fré Alexander Fedotov

Author:Pietro Giuseppe Fré, Alexander Fedotov
Language: eng
Format: epub, pdf
Publisher: Walter de Gruyter
Published: 2018-03-06T16:00:00+00:00

8.2.3.5Weights of the 4-dimensional spinor representation

The weights of the fundamental representation of 𝔰𝔭(4, ℂ) which corresponds to the spinor representation of 𝔰𝔬(3, 2, ℂ) ∼ 𝔰𝔬(5, ℂ) are easily read off from the explicit form of the matrix representation (8.115). They are listed below:

where the first column provides their components in the fundamental weight basis, while the second column gives their expression in an orthonormal basis. The weights are graphically shown in Figure 8.10.

Figure 8.10: The weights of the spinor representation of 𝔰𝔬(5) which is the fundamental representation of 𝔰𝔭(4). The shaded region is the Weyl chamber. One sees that the fundamental weight λ1 is just the highest weight of the spinor representation.

Download

Copyright Disclaimer:
This site does not store any files on its server. We only index and link to content provided by other sites. Please contact the content providers to delete copyright contents if any and email us, we'll remove relevant links or contents immediately.