Search Results
Search type | Search syntax |
---|---|
Tags | [tag] |
Exact | "words here" |
Author |
user:1234 user:me (yours) |
Score |
score:3 (3+) score:0 (none) |
Answers |
answers:3 (3+) answers:0 (none) isaccepted:yes hasaccepted:no inquestion:1234 |
Views | views:250 |
Code | code:"if (foo != bar)" |
Sections |
title:apples body:"apples oranges" |
URL | url:"*.example.com" |
Saves | in:saves |
Status |
closed:yes duplicate:no migrated:no wiki:no |
Types |
is:question is:answer |
Exclude |
-[tag] -apples |
For more details on advanced search visit our help page |
History and philosophy of mathematics, biographies of mathematicians, mathematics education, recreational mathematics, communication of mathematics.
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 …
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 …
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 …
48
votes
Fraktur symbols for Lie algebras
Some of what's been said so far about the history makes good sense, but by no means all. Let me add my own perspective, for what it's worth. The font called Fraktur by LaTeX (also known as "gothic …
3
votes
Linear Algebra classic books
A more "modern" book than those already mentioned is the one by Paul Halmos here. This was first published in 1942 in the Annals of Math. Studies series, with a later edition in 1958; that edition …
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 …
12
votes
Accepted
Who originated the standard symbols for Lie groups GL, SL, SU, etc.?
It's hard to provide definitive confirmation of Weyl's role, but his 1939 book was highly influential in all further developments. It's important to realize that notation (and terminology) in mathe …
18
votes
Accepted
Why are they called Specht Modules?
The question is interesting though perhaps not strictly "research-level". Terminology in mathematics develops a bit haphazardly, and sometimes things get misleading names. In this case the work of …
7
votes
Accepted
Origin of the term "weight" in representation theory
Robert Bryant's comment motivates me to mention the "weighty" historical monograph Emergence of the Theory of Lie Groups (Springer, 2000) written by Thomas Hawkins. As usual with terminology such as …
3
votes
History of Jordan Canonical Form?
As I pointed out in my comment, there are too many questions listed here. Maybe I can clarify the term "Jordan-Chevalley decomposition" in the last one. Besides the arXiv post by Danielle Couty an …
5
votes
Origin of the theorem on the existence of the smallest field of definition of an affine variety
As far as I can see, Weil was indeed the main source for this viewpoint on fields of definition in algebraic geometry. However, it may be hard to pin down the specific result quoted here in his 1935 …
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 …
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 …
6
votes
What to do with antique math books?
Though I haven't dealt directly with them, I'm aware of another established company (in Ohio) which buys and sells advanced or rare books in mathematics: http://www.zubalbooks.com/in …
31
votes
How might M.C. Escher have designed his patterns?
The June/July 2010 issue of the AMS Notices here has a further article by Doris Schattschneider (a graduate school classmate of mine) on Coxeter and Escher. Doris has written extensively about Esche …