In mathematics, the representation theory of the symmetric group is a particular case of the representation theory of finite groups, for which a concrete...

automorphism groups, and their representation theory. For the remainder of this article, "symmetric group" will mean a symmetric group on a finite set. The symmetric...

as a group with certain generators and relations. They are studied in combinatorics and representation theory. A finite symmetric group consists of all...

In the mathematical field of representation theory, group representations describe abstract groups in terms of bijective linear transformations of a vector...

this ring plays an important role in the representation theory of the symmetric group. The ring of symmetric functions can be given a coproduct and...

The representation theory of groups is a part of mathematics which examines how groups act on given structures. Here the focus is in particular on operations...

representations in the representation theory of the symmetric group, or in the area of algebraic combinatorics dealing with Young tableaux and symmetric polynomials...

historically the first) is the representation theory of groups, in which elements of a group are represented by invertible matrices such that the group operation...

In the mathematical field of representation theory, a weight of an algebra A over a field F is an algebra homomorphism from A to F, or equivalently, a...

MR 0513828 James, Gordon; Kerber, Adalbert (1981), The representation theory of the symmetric group, Encyclopedia of Mathematics and its Applications, vol. 16...

exponential. The full finite-dimensional representation theory of the universal covering group (and also the spin group, a double cover) SL ( 2 , C ) {\displaystyle...

A symmetric space is, in differential geometry and representation theory, a smooth manifold whose group of symmetries contains an "inversion symmetry"...

representations of the affine Hecke algebras at roots of 1 (generalising results of Kazhdan and Lusztig), the representation theory of the symmetric groups Sn in...

The second tensor power of a linear representation V of a group G decomposes as the direct sum of the symmetric and alternating squares: V ⊗ 2 = V ⊗...

of the group algebra of the symmetric group S n {\displaystyle S_{n}} whose natural action on tensor products V ⊗ n {\displaystyle V^{\otimes n}} of a...

In mathematics, and especially the discipline of representation theory, the Schur indicator, named after Issai Schur, or Frobenius–Schur indicator describes...

to the setting of pseudo-Riemannian manifolds. From the point of view of Lie theory, a symmetric space is the quotient G / H of a connected Lie group G...

useful in representation theory and Schubert calculus. It provides a convenient way to describe the group representations of the symmetric and general...

is isomorphic to a subgroup of a symmetric group. More specifically, G is isomorphic to a subgroup of the symmetric group Sym ⁡ ( G ) {\displaystyle \operatorname...

Modular representation theory is a branch of mathematics, and is the part of representation theory that studies linear representations of finite groups over...

They play an important role in the representation theory of the symmetric group. They generate a commutative subalgebra of C [ S n ] {\displaystyle \mathbb...

mathematical theorem in representation theory that relates irreducible finite-dimensional representations of the general linear and symmetric groups. Schur–Weyl duality...

group Representation theory of the Lorentz group Representation theory of the Poincaré group Representation theory of the symmetric group Ribbon theory a...

representation may refer to: A group action, see also Permutation representation A representation of a symmetric group (see Representation theory of the...

relies on a fact from representation theory. The weights of an irreducible representation of a connected compact semisimple group K with highest weight...

In abstract algebra, group theory studies the algebraic structures known as groups. The concept of a group is central to abstract algebra: other well-known...

characters of symmetric groups and the ring of symmetric functions. It builds a bridge between representation theory of the symmetric groups and algebraic combinatorics...

subrepresentations of the action of the symmetric group on the ring of polynomials, as discussed in representation theory of the symmetric group. Alternating...

normal 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...

n, or the alternating group on n letters and denoted by An or Alt(n). For n > 1, the group An is the commutator subgroup of the symmetric group Sn with...