Questions tagged [ade-classifications]
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14 questions
3
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1
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Classification of "homogeneous" submanifolds of ℝⁿ
I define a subset $M$ of $\mathbb R^n$ to be a "homogeneous Euclidean manifold" if:
it is a closed connected smooth submanifold of $\mathbb R^n$,
for every $p, q$ in $M$, there is a ...
- 245
3
votes
0
answers
105
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p-adic analogue of classification of irreducible Riemannian symmetric spaces?
For Riemannian symmetric spaces, we have a nice result that the simply-connected ones are products of irreducible symmetric spaces, of which we have a list of ten infinite families and some ...
- 568
0
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1
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190
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dimension vector of indecomposable module over preprojective algebra
It is well-known that there are finitely many indecomposable module over the preprojective algebra associated to a quiver $Q$ if and only if $Q=A_2,A_3,A_4$ and tame type for $A_5$ and wild for others....
- 849
11
votes
1
answer
322
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equivariant stable class of quaternionic Hopf fibration in RO(G)-degrees of ADE-type
Does the quaternionic Hopf fibration possibly represent a non-torsion element in the $G$-equivariant stable homotopy groups of spheres, for $G$ a finite subgroup of $SO(3)$ and in RO(G)-degree being ...
- 19.8k
10
votes
2
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363
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Symmetries of module categories over the category of representations of quantum $sl(2)$
The category $\mathcal{C}_l$ of tilting modules of the quantum group $U_q(sl_2)$ quotiented out by the modules of zero quantum dimension has a natural structure as a semisimple monoidal category when ...
- 103
4
votes
1
answer
497
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Kodaira classification and the McKay correspondence
Kodaira's table of singular fibers has a singular fiber
for each of $\tilde{A}_n$, $\tilde{D}_n$, $\tilde{E}_6$, $\tilde{E}_7$, and $\tilde{E}_8$; these are chains or cycles of (-2)-curves connected ...
3
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0
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390
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Blowing up a projective surface
Let $X$ be a smooth degree $d$ ($d>5$) surface in $\mathbb{P}^3$. We now blow up $X$ at a point, embed it in some projective space, and and consider a projection of it into $\mathbb{P}^3$. The ...
- 1,040
10
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1
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1k
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Du Val singularity of type G=A,D,E and "small" representations of G
We all know that a simple singularity $W_G(x_1,x_2,x_3)=0$ of type G=A,D,E has the following nice deformation involving the Cartan subalgebra $\mathfrak{h}$ of the Lie algebra $\mathfrak{g}$ of $G$. ...
- 6,123
0
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1
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What is your favorite ADE-style classification? [duplicate]
Possible Duplicate:
ADE type Dynkin diagrams
What is your favorite ADE-style classification?
Here ADE style is to be understood in a very broad sense. A classification which is not precisely ...
12
votes
2
answers
2k
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Integral positive definite quadratic forms and graphs
Let me start with a question for which I know the answer. Consider a symmetric integral $n\times n$ matrix $A=(a_{ij})$ such that $a_{ii}=2$, and for $i\ne j$ one has $a_{ij}=0$ or $-1$. One can ...
- 13.1k
33
votes
4
answers
7k
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Classification of finite groups of isometries
Consider the problem of classifying the finite groups of isometries of $\mathbb{R}^n$.
For $n=2$ it is cyclic and dihedral groups.
For $n=3$ they are well known, probably from Kepler and are related ...
35
votes
1
answer
3k
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Is there a common genesis for ADE classifications?
Recall that a certain type of object admits an ADE classification if there is a notion of equivalence relative to which equivalence classes of objects of the given type can be placed in one-to-one ...
- 29.2k
26
votes
1
answer
2k
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Does the quantum subgroup of quantum su_2 called E_8 have anything at all to do with the Lie algebra E_8?
The ordinary McKay correspondence relates the subgroups of SU(2) to the affine ADE Dynkin diagrams. The correspondence is that the vertices correspond to irreducible representations of the subgroup, ...
- 28.1k
35
votes
17
answers
3k
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ADE type Dynkin diagrams
The ADE type Dynkin diagrams seem to come up in seemingly different areas of math. Two places they come up are:
(1) Classification of simply laced complex simple lie algebras.
(2) Finite subgroups ...
