11,605 reputation
236106
bio website mit.edu/~darij/www
location Karlsruhe (home), Munich (until summer 2011), Cambridge/MA (2011-)
age 26
visits member for 5 years
seen 6 hours ago
I'm just here for asking stupid questions.

14h
comment Hopf structures on “pictorial” descriptions of permutations
Oh! Sorry for this; I read "plane" and thought this had to be something different.
16h
comment Hopf structures on “pictorial” descriptions of permutations
Are you aware of the Hopf algebra of double posets? (See Malvenuto & Reutenauer, A self paired Hopf algebra on double posets and a Littlewood–Richardson rule.) The Malvenuto-Reutenauer Hopf algebra is a subquotient of it (it is actually a quotient of the Hopf algebra of special double posets), and it is defined in a way which does not involve the labels 1,2,...,n.
Dec
16
comment Arithmetic product of symmetric functions: why is it integral?
Thanks once again. The integrality statement is now in Exercise 4.33 of Vic Reiner's and my Hopf notes web.mit.edu/~darij/www/algebra/HopfComb-sols.pdf (and the induction formula is in its solution -- although I had to rule out the case when $n$ or $m$ is $0$ first because we don't currently treat induced characters over noninjective morphisms). Incidentally, do you happen to know how to prove (or disprove) the very similar question mathoverflow.net/questions/182083 ?
Dec
14
comment Central idempotents from characters in Frobenius algebras (generalizing Lusztig arXiv:math/0208154v2 §19)
@JimHumphreys: Thanks for the pointer to $U_p\left(\mathfrak{g}\right)$ ! They sound like they could lead to some nice counterexamples (or, failing it, examples). The question is this long because I use it as a dumping ground for proofs...
Dec
14
revised Central idempotents from characters in Frobenius algebras (generalizing Lusztig arXiv:math/0208154v2 §19)
reference updated, typos fixed, two new facts
Dec
12
awarded  Yearling
Dec
8
comment A question about symmetric matrix
You sound like you have decided to never write more than one book.
Dec
6
awarded  Enlightened
Dec
6
awarded  Nice Answer
Dec
6
answered A question about symmetric matrix
Dec
6
comment A question about symmetric matrix
OK, but on math.stackexchange. :P
Dec
6
comment A question about symmetric matrix
Google "Birkhoff-van Neumann theorem".
Dec
2
comment Most harmful heuristic?
I am not quoting anything. I am merely trying to clarify that both of my sentences are part of the false heuristic, rather than the first being the false heuristic and the second being its refutation. Maybe I should have used parentheses, but I don't want to be that guy.
Dec
2
comment “Nyldon words”: understanding a class of words factorizing the free monoid increasingly
See the last two comments by user38477 under his answer; they refer to your post.
Nov
29
comment Examples of common false beliefs in mathematics
The uncountably many elements $1/(x-a)$ for all $a \in \mathbb C$ are linearly independent.
Nov
28
comment “Nyldon words”: understanding a class of words factorizing the free monoid increasingly
OK, now this means a lot of reading-up for me... once the FPSAC deadline is over. Sorry for the slowness.
Nov
26
comment Apocryphal Maschke theorem?
It is -- but seeing why is so is part of the problem.
Nov
26
comment Apocryphal Maschke theorem?
@WillSawin: I want an iso of k[G]-bimodules, not of bimodules over different algebras (whatever that would be). The k[G]-bimoudle structure on the sum of the End-rings doesn't a priori look canonical. Anyway the answers spread given are simple enough -- I have bumped the question only to fix an error in my post and bad latex in an answer.
Nov
26
revised Apocryphal Maschke theorem?
throw away some trash
Nov
26
revised Apocryphal Maschke theorem?
something broke the latex