Explore: Representation Of The Symmetric Group

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

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

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

natural representation of the symmetric group Sn in n dimensions by permutation matrices, which is certainly faithful. Here the order of the group is n!

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

complex (hermitian), and if the indicator is −1, the representation is quaternionic. All representation of the symmetric groups are real (and in fact rational)

irreducible representation of a compact group on a complex vector space has. It can be used to classify the irreducible representations of compact groups on real