Timeline for Reference request: Models of cuspidal representations of GL(n,k) where k is a finite field
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Jan 31, 2018 at 11:18 | vote | accept | Q-Zh | ||
| Jan 24, 2018 at 20:56 | comment | added | Jim Humphreys | @LSpice: As I recall, he started to keep both the publication list and the list of his own comments on some of them at his homepage, but recently the comments got transferred to the arXiv. Anyway, these comments are often quite useful for putting his papers in context. He has been remarkably productive for many decades, but sometimes his papers are hard to unpack even though they have many unexpected gems tucked away inside. | |
| Jan 24, 2018 at 16:41 | comment | added | LSpice | Does Lusztig more regularly update the comments on his papers on his web-site, or on the arXiv? Anyway, it may be worth knowing that some set of comments is available at www-math.mit.edu/%7Egyuri/pub.html . (This is an amazing resource, wherever you find it.) | |
| Jan 21, 2018 at 14:43 | history | edited | Jim Humphreys | CC BY-SA 3.0 |
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| Jan 13, 2018 at 16:12 | comment | added | Jim Humphreys | @QingZhang: This approach is admittedly indirect but does yield an explicit construction of a typical irreducible representation with a cuspidal character over $\mathbb{C}$. It might help to look at Lusztig's own comments on this paper, which is [17] on his list: arxiv.org/pdf/1707.09368.pdf (But to go further with groups of Lie type, one mainly relies on the characters.) | |
| Jan 13, 2018 at 6:32 | comment | added | user148212 | @QingZhang It is a complex rep as $\bar{Q}_p$ is isomorphic to $\mathbb{C}$ as abstract fields. | |
| Jan 13, 2018 at 5:17 | comment | added | Q-Zh | I could not find the book by Lusztig at this moment. The following is a description of the book taken from press.princeton.edu/titles/1464.html The book gives an explicit construction of one distinguished member, $D(V)$, of the discrete series of $GL_n (F_q)$, where $V$ is the n-dimensional $F$-vector space on which $GL_n(F_q)$ acts. This is a p-adic representation; more precisely $D(V)$ is a free module of rank $(q--1) (q^2—1)...(q^{n-1}-1)$ over the ring of Witt vectors $W_F$ of $F$. It seems that this is not complex representation I need. | |
| Jan 12, 2018 at 12:57 | history | answered | Jim Humphreys | CC BY-SA 3.0 |