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1d
comment Can the product of a simple and a non-simple indecomposable representation be semisimple?
As Jim Humphreys suggests, it would be helpful to know what kind of "generic irreducible representations" $\sigma$ you are considering? Do they have any special properties? The fact that you have information about the semi-simplicity of $\rho\otimes\sigma$ leads me to think there is more relevant information available.
Jun
26
comment Permutation covering of a $G$-lattice
Ahhh! I have been using the diagonal action of $C_p$ on $L$ to make computations.
Jun
25
comment Permutation covering of a $G$-lattice
I am having a bit of trouble verifying your answer. In particular, I don't see why $L$ has no invariant subspaces. For example, when $p=3$, I calculated that $L$ has exactly two 1-dimensional submodules. This means there should be a permutation covering of rank $5$. Am I missing something here?
Jun
2
awarded  Citizen Patrol
Apr
8
comment An application of Maschke's theorem
@KConrad $7\cdot 7 = 49 = (5\sqrt{2}-1)(5\sqrt{2}+1)$?
Mar
3
awarded  Yearling
Nov
21
comment “Nyldon words”: understanding a class of words factorizing the free monoid increasingly
Also, can you define you ordering more explicitly. Do you read words left-to-right or right-to-left?
Nov
21
comment “Nyldon words”: understanding a class of words factorizing the free monoid increasingly
I don't think your comment above is helpful. I think it was appropriate to delete it.
Nov
21
comment “Nyldon words”: understanding a class of words factorizing the free monoid increasingly
Isn't (3) already false for $w=101$, $u=10$ and $v=1$?
Nov
20
comment “Nyldon words”: understanding a class of words factorizing the free monoid increasingly
@TheMaskedAvenger This is definitely not what is going on. The modifications you are proposing would yield Lyndon words for the associated ordering. Nyldon words behave very differently. For example, the Nyldon words $101$ and $1011$ defy this kind of description.
Nov
18
comment “Nyldon words”: understanding a class of words factorizing the free monoid increasingly
@darijgrinberg: sorry, no. I was not saying that. I was just pointing out that things that seem to happen in a 2 letter alphabet are unlikely to be true for bigger alphabets. For example, certain palindromes are Nyldon, but cycling the first letter to the end will not make them Lyndon Honestly, these Nyldon words are baffling.
Nov
18
comment “Nyldon words”: understanding a class of words factorizing the free monoid increasingly
@PerAlexandersson, I don't think this coincidence in a 2 letter alphabet generalizes. The thing about Lyndon words is that they are filled with patterns. For example, every Lyndon work looks like $w=w_1^kw_1'i$, where $w_1$ is Lyndon, $w_1'$ is a (possibly empty) left factor of $w_1$ and $i$ is a letter such that $w_1'i>w_1$ (this was proved by Leclerc). In contrast, Nyldon words seem to be pattern avoiding.
Nov
7
comment Irreducible representations of Weyl group of F$_4$ on zero weight spaces?
I don't have Bourbaki with me. Is $\varpi_1$ short or long?
Nov
3
answered Given a locally nilpotent derivation over a field of characteristic 0 and a local slice, how is the ring homomorphism below defined?
Nov
2
comment When exactly and why matrix multiplication became a part of undergraduate curriculum?
Just to focus in, is your question about when US universities adopted linear algebra in their core curriculum? And, if this can be established, who were the advocates of this that made it happen?
Nov
1
answered The formula for a perhaps basic identity (move from stackexchange)
Oct
31
awarded  Yearling
Oct
22
answered Does Schur's Lemma hold in this case? Regular representations of $S_n$ over $\mathbb R$
Oct
18
revised Homomorphisms from irreducible spaces to reducible spaces
added 25 characters in body
Oct
18
answered Homomorphisms from irreducible spaces to reducible spaces