# Questions tagged [exceptional-groups]

Exceptional Lie groups G2, F4, E6, E7, E8 of dimensions 14, 52, 78, 133, 248 were obtained as result of classification of simple Lie groups performed by Killing and Elie Cartan. The tool used in classification is Dynkin diagram and root system of vectors in Lie algebra of the group. The remaining Lie groups form four infinite families of transformations of n-dimensional space over real (odd and even), complex and quaternionic field.

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### How to describe the compact real forms of the exceptional Lie groups as matrix groups?

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### How to check whether a given matrix is in the image of a representation?

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### Reference request: Commutator relations for the exceptional group F4

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### $8 \times 31 = 8 \times 31$?

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### Branching rules for E6 into SU(3)^3

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### Does the 3875-dimensional rep of $E_8$ have a solution to $x\star x=0$?

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### Orbits of action of the split group of type $F_4$

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### Better names for Lie groups

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### Flag manifolds as incidence correspondences

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### Dimensions of $E_{7\frac{1}{2}}$

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### The Grassmannian Gr(2,8) and an E7 surprise

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### Does Deligne's exceptional series lead to an “exceptional K-theory”?

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### Adjoint orbits of a finite group of type $G_2$ [reference request]

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### Freudenthal geometries for exceptional simple Lie groups

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### Concrete description of an exceptional minuscule variety

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### The double cover of $[W(E_7),W(E_7)] \cong Sp_6(\mathbb F_2)$ as a Galois group over $\mathbb Q$

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### Constructing $E_8$ from its branching to $A_8$

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### Constructing real forms of the Tits-Freudenthal magic square for (Rosenfeld) projective planes

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### A question on complex semisimple Lie groups and $(\mathbb{C}^2, \omega)$

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### Where can I find details of Elie Cartan's thesis?

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### What is the stabilizer of the following $7$-dimensional cross-product?

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### What is the largest subgroup of $GL^{+}(7,\mathbb{R})$ which smoothly retracts onto $G_2$?

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### Exceptional symmetric spaces with quaternionic structure

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### A few questions about $E_7$ and its symmetric spaces

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### A few questions about $E_6$ and its symmetric spaces

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### Describing the action of $^2E_6(q)$

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### A representation of Spin(9,1)

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### Decomposition into irreducible components of a representation of $Spin(9)$

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### Explicit generators of the Lie algebra $spin(9)$

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### Exceptional symmetric spaces embedded in exceptional Lie group

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### Transitivity of $Spin(7)$ in triples of vectors

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### The special embedding $\mathfrak{so}(7)\subset\mathfrak{so}(8)$

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### Is this characterization of (-1)-eigenspaces of the Weyl group of $E_6$ known?

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### How the exceptional simple Lie groups/ algebras were first discovered and by whom?

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### $Spin(7)$ as stabilizer of a $4$-form revisited

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### $Spin(7)$ as stabilizer of a $4$-form

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### Decomposition of $S^7=Spin(7)/G_2$

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### Construction of Thom-Spectrum for G_2-Structures

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**23**

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### Triality of Spin(8)

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### Groups that do not exist

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### Irreducibility of fundamental Weyl modules

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### Is the derived group of $G_2$ simply connected?

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### Is there a connection between exceptional Galois groups and Ramanujan's partition congruences

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### $G_2$ and Geometry

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### Does $\mathrm{E}_7/(\mathrm{SU}_8/(\mathbb{Z}/2))$ carry an almost complex structure?

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### How do Jordan algebras help one understand representations of exceptional Lie algebras?

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### Geometric interpretation of exceptional Symmetric spaces

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### Matrix representation for $F_4$

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