2
votes
2answers
555 views
about state-field correspondence
In the defination of vertex algebra,we call the vertex operator state-field correspondence,does that mean that it is an injective map??
Are there some physical intepretations about …
0
votes
1answer
491 views
Is it useful to consider cohomology of group representations?
In group representation theory, one attempts to explain and classify (some of) the modules over the group ring $k[G]$, for some field $k$. In group cohomology, one develops the mac …
0
votes
3answers
525 views
Skewing the distribution of random values over a range
The following code comment comes from PHP, a free and open source project. I have done my own research and I cannot find any evidence to support the argument made in this code c …
2
votes
1answer
526 views
Maximal subfield inside a central division algebra
D is a central division algebra over F. We know that we can always find a maximal subfield K inside D such that K/F is separable. I want to know can we always make it Galois?
8
votes
2answers
339 views
Primacy of arcs/arrows over vertices/objects
Freyd's Abelian Categories is the only textbook I know where the primacy of arrows over objects is taken seriously already in the axioms: there is no talk of objects at all. Only l …
3
votes
2answers
334 views
Comparing lower central series and augmentation ideal completions
Let G be a group. Let $G^p$ be the completion of G with respect to the mod p lower central series of G.i.e. $G^p=\varprojlim_{q} G/\gamma_qG$, where $\gamma_qG$ is generated by all …
-1
votes
1answer
301 views
Conditional expectation [closed]
Given E[v|X=x]=g[x] and the pdf of X (f[x]), how to calculate E[v|x>=x0]? The pdf of V or the joint pdf of V,X are unknown. My guess is that this problem has no solution.
0
votes
1answer
156 views
Partitioned Runge-Kutta (Lobatto IIIAB)
I am wondering, if anybody knows some paper, that study convergence and stability of Partitioned Rung-Kutta Methods (especially Lobatto IIIAB) applied on separable Hamiltonian syst …
5
votes
2answers
637 views
Characterization of Riemannian metrics
This is probably an insanely hard question, but given an abstract metric space, is there some way to determine whether it's a manifold with a Riemannian, or more generally a Finsle …
0
votes
0answers
414 views
What’s the homology of classifying space of symmetric group with coefficient $Q$ [closed]
Or what's the classifying space of symmetric group? Thanks!
10
votes
3answers
726 views
How does one find vanishing algebraic cycles?
I have a question, related to what I asked before.
Let's consider a smooth hyperplane section $X$ of a smooth projective variety $Y$ over $\mathbb C$.
According to Weak Lefschetz t …
6
votes
0answers
289 views
A partition problem.
Denote by $\omega_{d,n}(N)$ the number non-negative integer solutions of the following system of equations:
\begin{gather*}
\alpha_1+2 \alpha_2+\cdots+d \alpha_d=N,
\end{gathe …
4
votes
2answers
679 views
when are epimorphisms of algebraic objects surjective?
let $C$ be the category of $\tau$-algebras for some type $\tau$. consider the statements:
every monomorphism is regular.
every epimorphism in C is surjective.
it is easy to see …
2
votes
1answer
338 views
derivative in the ring k[e]/e², chain rule
Let $k$ be a ring and $\overline{k} = k[\epsilon]/\epsilon^2$. For every $f \in k[t]$ there is a unique $f' \in k[t]$ such that $f(t+\epsilon)=f(t)+\epsilon f'(t)$ holds in $\overl …
1
vote
2answers
1k views
The meaning of an intertwiner?
I think that a reformulation of my question is necessary:
An intertwiner $\iota:\; V_{j_{1}}\bigotimes V_{j_{2}}\rightarrow V_{j_{3}}$ is defined as:
$\forall g\in SU(2),\;\forall …
