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1d
comment What is Koszul dual of a curve?
See also: Inamdar, Mehta, Frobenius splitting of Schubert varieties and linear syzygies. American Journal of Math.
1d
comment What is Koszul dual of a curve?
Great question! This paper of Bezrukavnikov arxiv.org/abs/alg-geom/9502021 (apparently never published?) is relevant for $\mathbb{P}^1$.
Jan
22
awarded  Nice Answer
Jan
21
comment An analogue of Deligne--Lusztig theory for real groups?
I just realised that I am repeating myself: mathoverflow.net/questions/109461/…
Jan
21
comment An analogue of Deligne--Lusztig theory for real groups?
I find it helpful to think about $\mathbb{P}^1 \setminus \mathbb{P}^1(\mathbb{F}_q)$ as somewhat analogous to the upper half plane (or perhaps more precisely the upper and lower half planes $\mathbb{P}^1 \setminus \mathbb{P}^1(\mathbb{R})$). In case of finite reductive groups one gets interesting representations (Drinfeld's observation), and holomorphic sections for $SL_2(\mathbb{R})$ gives the discrete series. Beyond that I have no idea. I guess these ideas are not pursued as much because BB localisation gives a pretty convincing picture for real groups.
Jan
10
reviewed Approve The projection of density $1$ point on a rectifiable set
Nov
21
awarded  Custodian
Nov
3
revised Example to show that the inverse image under a finite morphism is not t-exact with respect to the perverse t-structure
added 42 characters in body
Nov
3
comment Example to show that the inverse image under a finite morphism is not t-exact with respect to the perverse t-structure
Of course you are right... I won't change the above as your example is correct.
Nov
3
comment Recovering representation from its character
I think the formula for the primitive central idempotent should read $\pi = \chi(1)/|G| \sum \chi(g^{-1})g$.
Oct
21
awarded  Yearling
Sep
5
comment Jordan-Hölder-like statements for modules with $\Delta$-filtrations over a quasihereditary algebra
Yes, $\Delta$-filtrations are essentially unique (more precisely, the filtration indexed by ideals in the poset $\Lambda$ is unique). I don't know a reference but the proof isn't difficult. I don't understand your second question. What does "with the property as above" mean?
Aug
5
comment Is it possible to classify the indecomposable representations of the wild quiver with one vertex and two arrows using infinite sets of parameters?
You should also define what you mean by $\mathbb{F}_2$. I guess you mean the quiver with one vertex and two arrows?
Jul
27
comment Is there a structure theorem or group law for finite groups generated by two elements?
mathoverflow.net/questions/59213/…
Jul
15
comment Is there a topological Chevalley-Shephard-Todd Theorem?
So now we arrive at the converse, and Jason's argument. I agree there is something left to show...
Jul
15
comment Is there a topological Chevalley-Shephard-Todd Theorem?
@Nico: so now I think I understand better: the quotient $\mathbb{C}^n \to \mathbb{C}^n/\Gamma$ is a quotient both in the category of topological spaces, and algebraic varieties. In particular, if $\Gamma$ is generated by pseudoreflections then it will be a topological manifold after all (by classical Chevalley-Shephard-Todd).
Jul
15
comment Is there a topological Chevalley-Shephard-Todd Theorem?
@Nico: Sorry, I wrote that comment after a glass of wine.
Jul
14
comment Is there a topological Chevalley-Shephard-Todd Theorem?
I don't know why there is a bounty ... it seems Jason has already answered the question!
Apr
17
awarded  Enthusiast
Apr
5
comment Cohomology of a local system and Deligne's weight filtration
@use54343: What do you mean by "your construction"? Restricting $IC$ to a strata? Doesn't taking $\mathcal{L}$ to the the local system I describe (an $IC$) recover what you want. (It is not clear to me how your second paragraph relates to the first. It seems your question is simply a question about variations of mixed Hodge structures on $\mathbb{C}^*$ and their cohomology. It would be much clearer if stated in this way.)