Timeline for Representations of Pin vs. Representations of Clifford
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
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| Feb 24, 2023 at 1:26 | history | edited | darij grinberg | CC BY-SA 4.0 |
fixing the MO bug perhaps
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| Jul 9, 2010 at 15:12 | answer | added | user7219 | timeline score: 17 | |
| May 12, 2010 at 7:13 | comment | added | darij grinberg | Actually, Roe uses this to characterize the irreducible representations of the Clifford algebra. In my eyes this is quite an overkill, since it is easy to see that the representation map from the Clifford algebra to the endomorphism ring of the half-spin representation (or, in the odd case, to the sum of the endomorphism rings of the two half-spin representations) is bijective. | |
| May 11, 2010 at 23:52 | comment | added | Paul Siegel | I remember being really confused by this when I read that stuff awhile back, and I wound up turning to Spin Geometry by Lawson and Michelsohn in order to understand the construction of the spinor bundle. I guess I'm relieved I didn't dwell on it too much! Still, the only part of this discussion that is needed for the rest of the book is the existence and uniqueness of the spin representation in even dimensions, and uniqueness even survives the mistake. I think I'll discuss this with Prof. Roe when I see him again next week. | |
| May 11, 2010 at 15:43 | vote | accept | darij grinberg | ||
| May 11, 2010 at 15:22 | answer | added | S. Carnahan♦ | timeline score: 6 | |
| May 11, 2010 at 12:52 | answer | added | David E Speyer | timeline score: 14 | |
| May 11, 2010 at 10:57 | history | edited | darij grinberg | CC BY-SA 2.5 |
added 488 characters in body
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| May 11, 2010 at 8:14 | answer | added | skupers | timeline score: 1 | |
| May 11, 2010 at 6:44 | comment | added | darij grinberg | Every representation of Pin which has -1 acting as -id. (The others are clearly taboo.) | |
| May 11, 2010 at 1:21 | comment | added | Eric O. Korman | If I understand correctly, the question basically boils down to whether every rep of Pin is the restriction of a rep of Cl? | |
| May 10, 2010 at 23:55 | comment | added | Michael | For 3 -> 1, extend the induced map R^k --> End(V) using the universal property of Cl(R^k). | |
| May 10, 2010 at 23:38 | history | asked | darij grinberg | CC BY-SA 2.5 |