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Results tagged with ho.history-overview
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user 4231
History and philosophy of mathematics, biographies of mathematicians, mathematics education, recreational mathematics, communication of mathematics.
22
votes
4
answers
4k
views
How did "Ore's Conjecture" become a conjecture?
The narrow question here concerns the history of one development in group theory, but the broader context involves the sometimes loose use of the term "conjecture". This goes back to older work of …
- 52.9k
3
votes
0
answers
172
views
Origin of the standard result on convex hull of weights of an irreducible finite dimensional...
What is the earliest published statement and proof of the well-known result: for a simple Lie algebra over $\mathbb{C}$ or other algebraically closed field of characteristic 0, the convex hull (in the …
- 52.9k
6
votes
2
answers
1k
views
Convention about "long" roots for simple Lie algebras of types ADE?
The classification of simple Lie algebras (over $\mathbb{C}$ or other sufficiently large field of characteristic 0) correlates these Lie algebras with the irreducible reduced root systems (in Bourbaki …
- 52.9k
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
31
votes
4
answers
3k
views
What was Casimir's precise role in describing the center of the universal enveloping algebra...
This question is prompted by a recent MO question on explicit computations of Weyl group invariants for certain exceptional simple Lie algebras:
37602. Like some others who started graduate study in …
- 52.9k
65
votes
6
answers
9k
views
Origin of terms "flag", "flag manifold", "flag variety"?
These terms have become common in Lie theory and related algebraic geometry and combinatorics, as seen in many questions posted on MO, but it's unclear to me where they first came into use. Probably …
- 52.9k