All Questions
9 questions
18
votes
4
answers
5k
views
The only great book that Bourbaki ever wrote?
OK, the title is opinionated and contentious, but I have a definite
question. I know that the title refers to the Bourbaki volume
Groupes et Algèbres de Lie (Chapters 4-6), published in 1968, but
...
- 12.4k
18
votes
0
answers
612
views
Who first noticed the duality for finite groups?
A.A.Kirillov in section 12.3 of his "Elements of the Theory of Representations" writes that the first "symmetric" duality theory for non-commutative groups was the theory for finite groups. In short ...
- 7,426
15
votes
1
answer
961
views
Who conjectured the Cartan determinant conjecture
The Cartan determinant conjecture states that every finite dimensional algebra of finite global dimension has the property that the determinant of its Cartan matrix is equal to one. Who stated this ...
- 26.5k
12
votes
2
answers
702
views
Character theory and Quantum Chemistry
Who (presumably a chemist) realized first the efficiency of character theory in calculations of orbitals of atoms? In which year?
- 52.3k
12
votes
1
answer
1k
views
Smallest dimension of nontrivial representation of a simple Lie algebra over `$\mathbb{C}$`
The question involved here is natural and very classical, but I'm unsure what has been formally stated and proved in the literature. The only approach I know involves assembling facts that apparently ...
- 52.9k
11
votes
0
answers
870
views
Reference/quote request: "All of combinatorics is the representation theory of $S_n$"
I think I remember reading somewhere a glib (or is it deep?) quote, perhaps due to Rota?, which was something like
"All of combinatorics is essentially [or can be reduced to?] the representation ...
- 3,230
3
votes
2
answers
214
views
History of an open problem on partial tilting modules
The following is an open problem:
Given a partial tilting module $T$ over a finite dimensional algebra $A$ (that is $Ext_A^i(T,T)=0$ for all $i \geq 1$ and $pd(T) < \infty$), then $T$ is a tilting ...
- 26.5k
3
votes
0
answers
115
views
Reference for the Netto's theorem on the permutation groups which was mentioned in the paper of Frobenius
I'm trying to read 'Uber die Charaktere der mehrfach transitiven Gruppen' written by Frobenius.
There he mentioned some theorems of Netto.
I'm depending on the Google translator. and the translation ...
- 1,013
3
votes
0
answers
282
views
Galois correspondence subgroups/subsystems
In this paper (1998) by M. Izumi, R. Longo, S. Popa, there is the following result (page 49) on compact groups:
Lemma 3.16. Let $G$ be a compact group and $Rep(G)$ the category of finite ...
