Timeline for Connected compact Lie groups with Lie algebra so(4n, R)
Current License: CC BY-SA 3.0
11 events
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| Jan 10, 2015 at 14:12 | comment | added | Jim Humphreys | @Ilia: As Skip's answer to the related question you link indicates, the term "half-spin group" is also commonly used for what people also call "semi-spinor group". The classification for Lie groups (or equivalently for algebraic groups over a field like $\mathbb{C}$) is written down in a variety of textbooks, aside from older literature. | |
| Jan 10, 2015 at 13:18 | comment | added | Ilia Smilga | Thanks. Now that I know the name, I have found this question which may also be of interest: mathoverflow.net/questions/47901/occurrence-of-semi-spin-groups | |
| Jan 10, 2015 at 13:17 | history | edited | Ilia Smilga |
Added a tag
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| Jan 10, 2015 at 13:08 | comment | added | Robert Bryant | Also, these show up in the exceptional symmetric spaces. For example, $\mathrm{E}_7$ contains $\mathrm{SO}'(12)$ (which has $\mathrm{SU}(2)$ for commutator, so that $\mathrm{E}_7/\bigl(\mathrm{SO}'(12)\mathrm{SU}(2)\bigr)$ is the associated Wolf space, while $\mathrm{E}_8$ contains $\mathrm{SO}'(16)$ as a (maximal) symmetric subgroup, so that $\mathrm{E}_8/\mathrm{SO}'(16)$ is an irreducible symmetric space. | |
| Jan 10, 2015 at 13:00 | comment | added | Christian Nassau | (I'm commenting because these remarks are too trivial for an answer) | |
| Jan 10, 2015 at 12:59 | comment | added | Christian Nassau | And here's a computation of their homology: Baum, Brodwer: The cohomology of quotients of classical groups, Topology 3: 305-336, 1965. | |
| Jan 10, 2015 at 12:58 | comment | added | Christian Nassau | Here's a physics paper abut their role in string theory: Brett McInnis, The semispin groups in string theory, arxiv.org/pdf/hep-th/9906059v1.pdf | |
| Jan 10, 2015 at 12:57 | comment | added | Robert Bryant | I think that these two groups (which are isomorphic, of course) are generally denoted $\mathrm{SO}'(4m)$, where $n=4m$. At least, this is the notation I have seen in Wolf and Helgason. | |
| Jan 10, 2015 at 12:57 | comment | added | Christian Nassau | These groups are usually called "semi-spinor" groups and denoted $Ss^\pm(4n)$. | |
| Jan 10, 2015 at 12:46 | comment | added | YCor | One can also wonder what's its smallest faithful representation. | |
| Jan 10, 2015 at 12:38 | history | asked | Ilia Smilga | CC BY-SA 3.0 |