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## Tagged Questions

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### The orbit $(G\cdot X) \cap \mathfrak{t}$ for $X\in \mathfrak{t}$ singular

This question may be a simply problem for experts. Let $G$ be a connected compact Lie group and $T$ be its maximal torus. Let $\mathfrak{g}$ and $\mathfrak{t}$ be the corresponding …
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### Mappings between Banach spaces

What is the definition of an analytic mapping between two Banach spaces? This is a problem I ran into when solving an integral equation. One of the related coefficients is represen …
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### common roots of bivariate polynomial equations

Let $f(x,y)=0$ and $g(x,y)=0$ be bivariate polynomial equations where the polynomials have the same degree, say, $N\geq 3$. Furthermore, both of them have the same terms but differ …
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### Strict applications of deformation theory in which to dip one’s toe

I hesitate to ask a question like this, but I really have tried finding answers to this question on my own and seemed to come up short. I readily admit this is due to my ignorance …
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### expressing group elements as a product of elements of a generating set

Hi, I am a student teaching myself basic abstract algebra (group theory right now). I am working through Lang's "Undergraduate Algebra" together with Artin's "Algebra," and from La …
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### Physical invariants of Calabi-Yau manifolds and G2 manifolds

Physicists said that for a given Calabi-Yau 3-fold with the topological Euler number e, |e|/2 corresponds to the number of gdnerations of the elementary particles. My question i …
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### References request: representations of Heisenberg algebra.

Let $p_1, p_2, \ldots$, be the power sum symmetric functions. Let $p_n^* = n \frac{\partial}{\partial p_n}$. Then $$p_n^* p_m - p_m p_n^* = \delta_{m, n} 1.$$ Where could I find …
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### Where did Sophus Lie write the group commutator for two one parameter groups.

If $X,Y$ are vector fields and $\def\Fl{\operatorname{Fl}}\Fl^X_t$ and $\Fl^Y_t$ their local flows, let $[\Fl^X_t,\Fl^Y_t]:= \Fl^Y_{-t}\Fl^X_{-t}\Fl^Y_t\Fl^X_t$ denote the group co …
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### How can I find the center of a set of coordinates? (Or how to find Lex Luthor’s hideout)

I have an array of 150 coordinates with which to provide the highest probability "center". How would you solve for the center of a cluster of data points? Here's a map an example …
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### Is it possible to rephrase Rossmo’s Formula into Euclidean distances?

If so, can you show me how? Here's Rossmo's Formula on Wikipedia. I tried embedding images of the formula but I'm new here and that's not allowed. If you're not familiar with th …
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### Is the ideal of compact operators strongly Borel?

Let $H$ be a separable infinite dimensional Hilbert space. Denote by $\mathcal{B}(H)$ the space of bounded operators on $H$, and $\mathcal{K}(H)$ the ideal of compact operators. Wh …
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### For which sites are all constant presheaves separated?

I'm intererested in open surjective geometric morphisms induced by fibrations of sites $S\to T$ a la Moerdijk, but as a warm-up, let's consider the case $S \to \ast$. In the case t …
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### Spectral sequences: opening the black box slowly with an example

My friend and I are attempting to learn about spectral sequences at the moment, and we've noticed a common theme in books about spectral sequences: no one seems to like talking abo …