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0answers
5 views

Parabolic lie group and weights

My question is about root system in Lie Algebra. Let G be a semisimple Lie group and $\mathfrak{g}$ be its lie algebra and $P$ be a parabolic subgroup of $G$ and $\mathfrak{p}$, be its lie ...
0answers
11 views

Inequlities for averaging over partially ordered set

Let's start from a classical inequality: If $0\le a_1\le\cdots\le a_k$ and $0\le b_1\le\cdots\le b_k$ then $(a_1+\cdots+a_k)(b_1+\cdots+b_k)\le k(a_1b_1+\cdots+a_k b_k)$. It can be written also in ...
2answers
29 views

Pullback of a constant sheaf

Let $\varphi:X\to Y$ be a surjective morphism of schemes which are connected and of finite type. Let $A$ be an abelian group, $\mathscr{F}$ be the constant sheaf on $X$ with fibers $A$ and ...
0answers
14 views

0answers
51 views

How can I tell if the origin is in the convex hull of a set of points? [on hold]

I want to know how to tell if the origin is in the convex hull of a set of points. In particular, I really want to know a necessary condition for this in terms of which orthants the points are in. ...
0answers
185 views

Transfinite derivatives [migrated]

I don't know if this is exactly research level, as I am only starting college. But I feel like this is the best place to ask the question. We all know of 1st, 2nd, 3rd, nth derivatives. Is there a way ...
1answer
47 views

Finite dimension implies regularity

Let $\mathscr{D}'(\mathbb R)$ be the set of distributions on $\mathbb R$ and $X$ be a linear subspace of $\mathscr{D}'(\mathbb R)$, which is closed under translations, i.e., if $\varphi\in X$ and ...
0answers
38 views

0answers
57 views

Finding relations between invariant polynomials

Suppose I have an action of a linear reductive group ($GL(2,\mathbb{C})^2$ in this case) on a complex vector space (of dimension $16$) and I want to compute explicitly the ring of invariants of this ...
1answer
387 views

Institutional response to “Esquisse d'un programme”

It is well-known that Grothendieck's "esquisse d'un programme" was submitted in 1984 as part as the author's application for a permanent position of "Directeur de Recherche" at the C.N.R.S. (the main ...
1answer
91 views

Definability in HOD

Let $\mathfrak{M}$ be a countable transitive model of set theory, and consider HOD (the hereditarily ordinal definable elements of $\mathfrak{M}$). Let $x$ be an object $x \in HOD$. So $x$ is ...
0answers
62 views

1answer
66 views

Problem with understanding an equation

I have read the article Short-wavelength Spectral Properties of the Gravity Field from a Range of Regional Data Sets and I don't know how to interpret Equation (10) on page 630, because this equation ...

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