Young Diagram Calculator

⋮⋮Statistics▾

Size |λ| 0

Shape λ ( )

Conjugate λ′ ( )

∏ hook lengths 1

# standard SYT 1

Max entry m for SSYT

# semistandard SSYT 1

⋮⋮Lie Algebra Weight▾

Type: rank n:

Weight λ—

—

dim V^λ—

|Weyl orbit|—

Draw a Young diagram, then compute.

No decomposition computed yet.

⋮⋮Branching Rules▾

Rule:

Decomposes V^λ_GL restricted to the subgroup. Stable when ℓ(λ) ≤ n.

Draw a Young diagram, then compute.

⋮⋮Symmetric Functions▾

basis

Draw a Young diagram to expand.

⋮⋮Display Options▾

Show hook lengths Shade by hook length Show cell coordinates (r,c)

⋮⋮Actions▾

Complement uses a bounding box. Draw diagram first.

⋮⋮Input▾

Partition rows

Enter row lengths separated by commas, non-increasing.

Dynkin labels

Uses [a₁−a₂, ..., a_n−1−a_n, a_n].

⋮⋮Export▾

@misc{zhou2026youngdiagramcalculator,
  author = {Xiaoxiang Zhou},
  title = {Young Diagram Calculator},
  year = {2026},
  note = {Interactive web application}
}