11,972 reputation
337109
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
I'm just here for asking stupid questions.

9h
revised An (open?) problem about a sequence of nested sub-matrices 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 k-th 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 four-subspaces 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 Chevalley-Warning Theorem
How's that 150-page manuscript going along? That's something I'd happily read at least in parts...
Apr
8
awarded  Good Question
Apr
8
accepted Strange boundary-like map on tensor algebra: what is its kernel?
Apr
8
answered Strange boundary-like 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 ideal-theoretic equations, not just the zero locus. However, it being in a section on multiplicity-free 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 self-contained 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...