Changes

Jump to: navigation, search

Linear representation theory of symmetric group:S3

104 bytes added, 04:44, 17 June 2012
Schur functors corresponding to irreducible representations
{| class="sortable" border="1"
! Common name of representation !! Degree !! Square of degree !! Corresponding [[Unordered integer partition|partition]] !! [[Young diagram]] !! Formula for dimension of corresponding [[Schur functor]] applied to a vector space of dimension <math>d</math> !! Degree of representation times this dimension !! [[Formula for calculating effect of Schur functor on character]] if this Schur functor is applied to any (possibly unrelated) representation whose character is <math>\chi</math>
|-
| [[trivial representation]] || 1 || 1 || 3 || [[File:Youngdiag3.png|100px]] || <math>d(d+1)(d+2)/6</math> || <math>\frac{d(d+1)(d+2)}{/6}</math> || <math>(\chi(g)^3 + 3\chi(g^2)\chi(g) + 2\chi(g^3))/6</math>
|-
| [[sign representation]] || 1 || 1 || 1 + 1 + 1 || [[File:Youngdiag1-1-1.png|30px]] || <math>d(d - 1)(d - 2)/6</math> || <math>d(d - 1)(d - 2)/6</math> || <math>(\chi(g)^3 - 3\chi(g^2)\chi(g) + 2\chi(g^3))/6</math>
Bureaucrats, emailconfirmed, Administrators
38,910
edits

Navigation menu