bio  website  mit.edu/~darij/www 

location  Karlsruhe (home), Munich (until summer 2011), Cambridge/MA (2011)  
age  26  
visits  member for  5 years, 4 months 
seen  11 mins ago  
stats  profile views  12,212 
I'm just here for asking stupid questions.
9h

revised 
An (open?) problem about a sequence of nested submatrices and their determinant
edited tags 
Apr 16 
revised 
$S_k(x+y)S_k(x)S_k(y)$ where $S_k$ is symmetric polynomial
there is no such thing as "the kth symmetric polynomial" 
Apr 13 
comment 
classifying pairs of idempotent matrices
So you want to characterize $k$vector spaces with two projections. A projection is characterized by its image and its kernel, which have to be complementary subspaces. So a solution will follow from the solution to the foursubspaces problem (e.g., sciencedirect.com/science/article/pii/S0024379504002575 ) after throwing away the indecomposables where the appropriate pairs of subspaces are not complementary. Or am I off here? 
Apr 10 
revised 
On permutation of elements of two bases of a vector space (Greub´s book)
deleted 6 characters in body 
Apr 10 
comment 
Dividing by two in the category of vector spaces
Shouldn't $SL(V)$equivariant maps also be $GL(V)$equivariant at least in characteristic $0$ ? 
Apr 9 
comment 
Are plactic classes convex under the right weak Bruhat order?
No, wait, it wouldn't prove it. 
Apr 9 
comment 
Open problems in Euclidean geometry?
Frankly, many of these are not particularly interesting. Especially the feet of the angle bisectors are rather obscure objects in terms of standard triangle geometry (they have some interesting properties, such as the ones the Emelyanovy have proven, but they are no more natural than, say, the three excenters, the Brocard points, the points where the incircle touches the sides, the projections of the symmedian point on the sides, the vertices of the tangent triangle, etc.). 
Apr 9 
revised 
Open problems in Euclidean geometry?
formatting 
Apr 9 
comment 
Are plactic classes convex under the right weak Bruhat order?
Oh. It seems that if $u \leq v$ in the right weak Bruhat order, then the shape of the RSK insertion tableau $P\left(u\right)$ (weakly) dominates the shape of the RSK insertion tableau $P\left(v\right)$. Or so I understand Taskin's paper. This, of course, would immediately prove that plactic classes are convex... 
Apr 9 
comment 
Are plactic classes convex under the right weak Bruhat order?
Bump (oops). Taskin's arXiv:math/0509174v2, in its Definition 2.3, implicitly says that the "weak order" on the set of SYTs is a partial order. Doesn't this imply that plactic classes of permutations are convex? If so, then how is it proven? 
Apr 9 
comment 
Proofs of the ChevalleyWarning Theorem
How's that 150page manuscript going along? That's something I'd happily read at least in parts... 
Apr 8 
awarded  Good Question 
Apr 8 
accepted  Strange boundarylike map on tensor algebra: what is its kernel? 
Apr 8 
answered  Strange boundarylike map on tensor algebra: what is its kernel? 
Apr 5 
comment 
A vector version of the Segre embedding: what is the kernel of the ring map?
The appropriate reference in my edition of Goodman and Wallach (2009) seems to be Theorem 12.2.12. It actually does the idealtheoretic equations, not just the zero locus. However, it being in a section on multiplicityfree spaces seems to suggest that the proof uses characteristic $0$ in a nontrivial way. Then again, this is a book that proves PBW using Ado's theorem, so I am not surprised by some roundaboutness :) 
Apr 5 
comment 
A vector version of the Segre embedding: what is the kernel of the ring map?
Thanks for the other reference! 
Apr 5 
accepted  A vector version of the Segre embedding: what is the kernel of the ring map? 
Apr 4 
comment 
A vector version of the Segre embedding: what is the kernel of the ring map?
Surely I would not mind something selfcontained and elementary, but what you said is perfectly a good answer. 
Apr 4 
comment 
A vector version of the Segre embedding: what is the kernel of the ring map?
Ah, even better, what I want is the Theorem in §8.1 of his Chapter 13. Care to post this as an answer? 
Apr 4 
comment 
A vector version of the Segre embedding: what is the kernel of the ring map?
@AbdelmalekAbdesselam: Good reference! Procesi's "Lie Groups", on page 536, says that "the double standard tableaux in these elements $\overline{x}_{ij}$ with at most $m$ columns are a basis of the ring $A_m$", which at least sounds close to what I am looking for. I'll need to make sure that it means what I think it means... 