Linked Questions
12 questions linked to/from Who invented diagrammatic algebra?
48
votes
11
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In "splendid isolation"
While browsing the Net for some articles related to the history of the Whittaker-Shannon sampling theorem, so important to our digital world today, I came across this passage by H. D. Luke in The ...
48
votes
4
answers
5k
views
How to constructively/combinatorially prove Schur-Weyl duality?
How is Schur-Weyl duality (specifically, the fact that the actions of the group ring $\mathbb{K}\left[ S_{n}\right] $ and the monoid ring
$\mathbb{K}\left[ \left( \operatorname*{End}V,\cdot\...
21
votes
3
answers
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What are the current breakthroughs of Geometric Complexity Theory?
I've read from Wikipedia about Geometric Complexity Theory (GCT) which (if I understood correctly) is a program for coping with the $ P=NP $ problem using algebraic methods.
That program seems ...
47
votes
2
answers
4k
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The two ways Feynman diagrams appear in mathematics
I've heard about two ways mathematicians describe Feynman diagrams:
They can be seen as "string diagrams" describing various type of arrows (and/or compositions operations on them) in a monoidal ...
15
votes
3
answers
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Integration of a function over 7-sphere
Suppose we have $x_1^2 + y_1^2 + x_2^2 + y_2^2 + x_3^2 + y_3^2 + x_4^2 + y_4^2 = 1$ and we define $z_j = x_j + iy_j$, where $j = 1,\,2,\,3,\,4$.
The problem is finding or approximating the ...
8
votes
3
answers
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What is higher dimensional algebra?
Could anyone explain what higher dimensional algebra is?
I tried to look on the web but I couldn't find a satisfactory definition, the ones that I found are too vague. What I'm looking for is a good ...
5
votes
2
answers
1k
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Formula for n-th iteration of dx/dt=B(x)
Let $B(x)$ be infinitely differentiable with respect to $x$.
Drop the use of parentheses on $B$ to delimit the argument $x$
and use them instead to hold the order of the derivative with respect to $x$....
9
votes
2
answers
662
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Сlosed formula for $(g\partial)^n$
The objective is to obtain a closed formula for:
$$
\boxed{A(n)=\big(g(z)\,\partial_z\big)^n,\qquad n=1,2,\dots}
$$
where $g(z)$ is smooth in $z$ and $\partial_z$ is a derivative with respect to $z$.
...
7
votes
2
answers
916
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Rigorous definition of the commutator $[a(k_1), a^\ast(k_2)]$ of creation and annihilation operators in boson quantum field models
In their lecture notes "Boson Quantum Field Models" (in "Mathematics of Contemporary Physics", R.Streater (ed.)), Glimm and Jaffe define an annihilation operator $a(k), k \in \mathbb{R}$ on a certain ...
7
votes
3
answers
554
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GIT quotients for linear representations of $SL(2,\mathbb C)$
Let $V$ be the standard two-dimensional representation of $SL(2,\mathbb C)$ and let ${\rm Sym}^2V$ be its symmetric square. Let $n$ be a positive integer and consider the following two representations ...
3
votes
1
answer
188
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Generalized tensor-train decomposition
If $U\in\bigotimes_{k=1}^p\mathbb R^{n_k}$ and $U^{(k)}\in\mathbb R^{r_{k-1}}\otimes\mathbb R^{n_k}\otimes\mathbb R^{r_k}$ with$^1$ $$U_{i_1,\:\ldots\:,i_p}=\sum_{j_0=1}^{r_0}\cdots\sum_{j_p=1}^{r_p}U^...
5
votes
0
answers
225
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Schröder and graphical logic?
I was actually surprised by a comment by John Baez over at the n-Category Cafe about his surprise that Ernst Schröder, a mathematician of whom he had known through Schröder's work on mathematical ...