Reputation
3,304
Next privilege 5,000 Rep.
Approve tag wiki edits
Badges
11 33
Impact
~70k people reached

Apr
22
reviewed No Action Needed Eigenfunction basis of Laplacian on a manifold
Apr
19
awarded  Good Question
Apr
18
comment the root lattice, reflections, and a coxeter element
The subject of the paper by Christian (and Michael Cuntz) that I referred to in my previous comment is exactly the question of whether it is possible to find a poset associated to $H_4$ "whose ideal structure returns the notion and basic properties of non-nesting partitions".
Apr
18
reviewed Looks OK Hodge dual on hermitian manifold
Apr
18
comment the root lattice, reflections, and a coxeter element
There is a different paper of Christian's which is relevant to the motivation for the question: arxiv.org/abs/1212.2876. According to this paper, there is no reasonable candidate for a "poset of positive roots" in $H_4$ (though note that there are reasonable candidates for dihedral groups and for $H_3$, due to Drew Armstrong). Thus, the hope that one could carry out the procedure for non-crystallographic Coxeter groups seems doomed. (I still think it's an interesting question on its own merits, though.)
Apr
14
comment Schubert varieties and Young diagrams
Being the ouside corners of a Young diagram just means that you have some set of pairs $(i,\lambda_i)$, no two having the same values in the first coordinate or in the second coordinate, and such that if $i_1<i_2$, then $\lambda_{i_1}>\lambda_{i_2}$ (note: the inequalities go in opposite directions).
Apr
13
comment positivity of semicanonical basis
You probably meant to say that $f_Z$ is required to be in the image of $U\mathfrak n$. Without that, you wouldn't have uniqueness.
Mar
26
awarded  Notable Question
Mar
13
comment “Face” numbers for tropical Grassmannian G′_2,7 simplical complex ?
I am sorry if my comment struck you as overly negative. I am certainly happy that it did not deter you from continuing with MO! Your broader point ("one should refrain from discouraging opinions of the sort above, esp for newbies") is, I think, only half the story. Part of how MO works is by discouraging certain kinds of questions. While this question is not terrible, you have certainly asked other questions that are much more interesting! But I acknowledge that I may not have struck the balance particularly well in this case.
Mar
13
answered Motivation for the Preprojective Algebra
Dec
31
comment References about Hasse diagrams of root systems
This paper arxiv.org/abs/1306.1593 by Ringel describes the posets for all the classical types, and has nice pictures for the exceptionals.
Dec
30
comment Laurent and power series over the field with one element?
Dyckerhoff's paper arxiv.org/abs/1505.06940 says that finite $\mathbb F_1[[t]]$-modules should be considered as an $\mathbb F_1$ vector space (i.e. finite set with distinguished element $*$) together with a nilpotent endomorphism. (I guess this is a different paper from the one @darijgrinberg was looking at; the parts of the partition arise here as lengths of maximal paths to $*$.)
Dec
23
reviewed No Action Needed Automorphisms of Riemann Surfaces
Nov
14
reviewed Approve Inference using Topological Data Analysis: Is it worth it for a regular statistician to learn TDA?
Nov
11
reviewed Close When a compact topological manifold with boundary is a ball?
Nov
10
reviewed Reopen An open mapping theorem for homogeneous functions?
Nov
6
reviewed Leave Open Elementary chains in forcing extensions of $M_1$
Oct
30
reviewed Leave Open multiplicative functions of powers
Oct
30
reviewed Leave Open Distribution of $\max_{n \ge 0} S_n$, random walk
Oct
20
revised Lexicographic order on increasing $k$-tuples
fixing the corner case $a_k=n$