Explore: Representations Of Infinite Symmetric Groups

algebras, Cartan's theory of symmetric spaces, and Hermann Weyl's description of representations of compact and semisimple Lie groups using highest weights

Nevertheless, groups acting on other groups or on sets are also considered. For more details, please refer to the section on permutation representations. Other

{\displaystyle \operatorname {Sym} (n)} . Symmetric groups on infinite sets behave quite differently from symmetric groups on finite sets, and are discussed in

symmetric space is still symmetric, so we can reduce to the case of simply connected symmetric spaces. (For example, the universal cover of a real projective

most famous for his joint work with Sergei V. Kerov on representations of infinite symmetric groups and applications to the longest increasing subsequences

could implement braid groups, applications in cryptography have been suggested. In analogy with the action of the symmetric group by permutations, in various

can all be seen as groups endowed with additional operations and axioms. Groups recur throughout mathematics, and the methods of group theory have influenced

metacyclic subgroup such that the quotient is a subgroup of the symmetric group on 4 points. A finite group is a Frobenius complement if and only if it has a

relate mathematical group elements to symmetric rotations and reflections of molecules. Representations of groups allow many group-theoretic problems to

natural generalization of the notion of Riemannian symmetric space from real manifolds to complex manifolds. Every Hermitian symmetric space is a homogeneous