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...

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

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...

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...

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...

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

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

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

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

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

specifically in group theory, the character of a group representation is a function on the group that associates to each group element the trace of the corresponding...

be used to read off the list of simple Lie algebras and Riemannian symmetric spaces. Together with the commutative Lie group of the real numbers, R {\displaystyle...

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 group theory, Cayley's theorem, named in honour of Arthur Cayley, states that every group G is isomorphic to a subgroup of a symmetric group. More specifically...

permutation group Rank 3 permutation group Representation theory of the symmetric group Schreier vector Strong generating set Symmetric group Symmetric inverse...

as crystals and the hydrogen atom, may be modelled by symmetry groups. Thus group theory and the closely related representation theory have many important...

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...

In group theory, restriction forms a representation of a subgroup using a known representation of the whole group. Restriction is a fundamental construction...

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 ⊗...

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

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

most fundamental symmetric polynomials. Indeed, a theorem called the fundamental theorem of symmetric polynomials states that any symmetric polynomial can...

operator Representation theory of the symmetric group Representation theory of diffeomorphism groups Permutation representation Affine representation Projective...

the algebraic side, besides group theory and representation theory, lattice theory and commutative algebra are commonly used. The ring of symmetric functions...

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...

representation theory of the symmetric group and symmetric polynomials. Given a function in k {\displaystyle k} variables, one can obtain a symmetric...

In group theory, the quaternion group Q8 (sometimes just denoted by Q) is a non-abelian group of order eight, isomorphic to the eight-element subset {...

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