New answers tagged root-systems
11
votes
Where do root systems arise in mathematics?
They arise in the representation theory of quivers: Gabriel's theorem says that a connected quiver has finite representation theory type if and only if it is of type ADE, and then the indecomposable ...
16
votes
Where do root systems arise in mathematics?
I first came across root systems in the classification of finite reflection groups. A point group $\Gamma\subseteq\mathrm O(\Bbb R^n)$ is a reflection group if it is generated by reflections at ...
8
votes
Where do root systems arise in mathematics?
The eigenvalue distribution functions of random matrices in different universality classes are determined by the multiplicities of the restricted roots of the corresponding symmetric spaces, see ...
6
votes
Accepted
Multiplication factors in folding root systems and Lie algebras by automorphisms
Suppose we fold a root system $(\Phi,\Delta)$ to a root system $(\Phi^\sigma,\Delta^\sigma)$. There exists two conventions:
long roots of $(\Phi^\sigma,\Delta^\sigma)$ correspond to multiple roots in ...
- 1,897
2
votes
Accepted
Are isomorphic maximal tori stably conjugate?
$\DeclareMathOperator\GL{GL}\DeclareMathOperator\SL{SL}\DeclareMathOperator\PGL{PGL}\DeclareMathOperator\Gal{Gal}$Let $(B, S)$ be a Borel–torus pair in $G \mathrel{:=} \mathsf G_2$, let $\alpha_1$ be ...
- 11.4k
Top 50 recent answers are included