Timeline for Simple modules for $U_q(\mathfrak{sl}_n)$ at roots of unity
Current License: CC BY-SA 2.5
9 events
| when toggle format | what | by | license | comment | |
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| May 21, 2011 at 11:37 | answer | added | M T | timeline score: 5 | |
| Mar 3, 2011 at 13:57 | vote | accept | M T | ||
| Mar 2, 2011 at 15:56 | comment | added | M T | You're right, I need $N \geq 3$: when $N=2$ the PBW basis breaks down and the dimension formula is wrong. | |
| Mar 2, 2011 at 15:45 | comment | added | Jim Humphreys |
Thanks for adding more detail. By the way, it's usual to require $N \geq 3$ in this case, though Andersen and others have studied the extra complications when $N=2$ (or $N=3$ for type $G_2$). Even though $\mathfrak{sl}_n$ is fairly well-behaved, it's extremely hard in practice to work out explicit results about the (finite dimensional) simple modules for quantum groups even in terms of characters and dimensions when $n>4$'. The modular analogue also needs $N=p$` to be very large compared with the Coxeter number $n$.
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| Mar 2, 2011 at 14:57 | history | edited | M T | CC BY-SA 2.5 |
added 1102 characters in body; added 1 characters in body
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| Mar 2, 2011 at 13:24 | comment | added | Jim Humphreys | It's important to clarify the language, since the literature cited by me and David Hill goes in entirely different directions. The "small quantum group" seems to refer to the construction in Lusztig's important 1990 paper in J. Amer. Math. Soc.. | |
| Mar 1, 2011 at 23:52 | answer | added | Jim Humphreys | timeline score: 9 | |
| Mar 1, 2011 at 20:45 | answer | added | David Hill | timeline score: 4 | |
| Mar 1, 2011 at 19:54 | history | asked | M T | CC BY-SA 2.5 |