Young diagrams
E924200
Young diagrams are combinatorial diagrams consisting of left-justified rows of boxes that visually represent integer partitions and play a central role in the representation theory of symmetric and general linear groups.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Young diagrams canonical | 1 |
Statements (47)
| Predicate | Object |
|---|---|
| instanceOf |
combinatorial object
ⓘ
diagram ⓘ |
| associatedWith |
Schur functions
NERFINISHED
ⓘ
Young tableaux ⓘ semistandard Young tableaux ⓘ standard Young tableaux ⓘ symmetric functions ⓘ |
| conjugationActsOn | integer partitions ⓘ |
| conjugationCorrespondsTo | transposing rows and columns ⓘ |
| correspondsTo |
Ferrers diagram
ⓘ
partition written in nonincreasing order ⓘ |
| embeddedIn | integer lattice grid ⓘ |
| hasOperation |
conjugation
ⓘ
transpose ⓘ |
| hasParameter |
column lengths
ⓘ
number of boxes ⓘ row lengths ⓘ |
| hasProperty |
consists of unit boxes (cells)
ⓘ
rows are arranged in nonincreasing order of length ⓘ rows are left-justified ⓘ |
| hasVariant |
border strip diagram
ⓘ
shifted Young diagram ⓘ skew Young diagram ⓘ |
| introducedBy | Alfred Young NERFINISHED ⓘ |
| orientation |
columns extend downward from the top row
ⓘ
rows extend to the right from the left margin ⓘ |
| relatedTo |
Ferrers graph
NERFINISHED
ⓘ
hook-length formula ⓘ |
| represents | integer partition ⓘ |
| usedIn |
Littlewood–Richardson rule
NERFINISHED
ⓘ
algebraic combinatorics ⓘ branching rules for general linear groups ⓘ branching rules for symmetric groups ⓘ combinatorial representation theory ⓘ general linear group representation theory ⓘ representation theory ⓘ symmetric function theory ⓘ symmetric group representation theory ⓘ |
| usedToCount | standard Young tableaux ⓘ |
| usedToDescribe |
Young subgroup decompositions
ⓘ
Young symmetrizers NERFINISHED ⓘ hook-length formula applications ⓘ |
| usedToIndex |
Schur functors
NERFINISHED
ⓘ
Specht modules NERFINISHED ⓘ irreducible representations of symmetric groups ⓘ polynomial representations of general linear groups ⓘ |
| visualizes | partition of a positive integer ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.