Young Diagram Calculator
Pure Math Toolkit
·
Young Diagram
2
Calculator
· click cells to draw · click again to erase
Young Diagram
generalized
paper
shifted
Young boundary edit
( )
rows
×
cols
⋮⋮
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:
Aₙ 𝓈𝓁(n+1) / 𝓈𝓊(n+1)
Bₙ 𝓈𝓀(2n+1)
Cₙ 𝓈𝓅(2n)
Dₙ 𝓈𝓀(2n)
E₆
E₇
E₈
F₄
G₂
rank
n
:
gl
n+1
csp
Weight λ
—
Dynkin labels
—
dim V
λ
—
|Weyl orbit|
—
Dominant representative
Show on canvas
Show Weyl orbit
dot action
paper
shifted
table
Export orbit
Weight space decomposition
compute
export
Draw a Young diagram, then compute.
No decomposition computed yet.
Borel-Weil-Bott
compute
export
Draw a weight, then compute.
No Borel-Weil-Bott result computed yet.
⋮⋮
Branching Rules
▾
Rule:
GL(n) x GL(n) → GL(n)
O(n) x O(n) → O(n)
Sp(2n) x Sp(2n) → Sp(2n)
GL(n+m) → GL(n) x GL(m)
O(n+m) → O(n) x O(m)
Sp(2n+2m) → Sp(2n) x Sp(2m)
O(2n) → GL(n)
Sp(2n) → GL(n)
GL(n) → O(n) (Littlewood)
GL(2n) → Sp(2n) (Littlewood)
GL(2n) → O(2n) → GL(n)
GL(2n) → Sp(2n) → GL(n)
Source B:
rank n:
rank m:
blank = stable formula only
GL view:
paper
shifted
compute
export
Stable branching formula. Draw source A on the canvas, then compute.
Draw a Young diagram, then compute.
⋮⋮
Symmetric Functions
▾
N
infinite
basis
m_λ
p_λ
e_λ
h_λ
s_λ
linear
poly
export
Draw a Young diagram to expand.
⋮⋮
Display Options
▾
Show hook lengths
Shade by hook length
Show cell coordinates (r,c)
⋮⋮
Actions
▾
Conjugate λ′
Complement (in box)
Clear
Complement uses a bounding box. Draw diagram first.
⋮⋮
Input
▾
Partition rows
Draw
Enter row lengths in any order. Non-partition, zero, or negative rows open generalized view.
Dynkin labels
Draw
Uses [a
1
−a
2
, ..., a
n−1
−a
n
, a
n
].
⋮⋮
Export
▾
LaTeX
SVG
Copy shape
@misc{zhou2026youngdiagramcalculator, author = {Xiaoxiang Zhou}, title = {Young Diagram Calculator}, year = {2026}, note = {Interactive web application} }