The ade-classifications tag has no wiki summary.

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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 ...

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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 ...

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### Classification of finite groups of isometries

Consider the problem of classifying the finite groups of isometries of R^n.
--For n=2 it is cyclic and dihedral groups.
--For n=3 they are well known, probably from Kepler and are related to ...

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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, ...

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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 $G$. ...

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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 ...

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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 ...

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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 ...

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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 ...