Identifier
Identifier
Values
[2] generating graphics... => 10
[1,1] generating graphics... => 5
[3] generating graphics... => 20
[2,1] generating graphics... => 16
[1,1,1] generating graphics... => 0
[4] generating graphics... => 35
[3,1] generating graphics... => 35
[2,2] generating graphics... => 14
[2,1,1] generating graphics... => 0
[1,1,1,1] generating graphics... => 0
[5] generating graphics... => 56
[4,1] generating graphics... => 64
[3,2] generating graphics... => 40
[3,1,1] generating graphics... => 0
[2,2,1] generating graphics... => 0
[2,1,1,1] generating graphics... => 0
[1,1,1,1,1] generating graphics... => 0
[6] generating graphics... => 84
[5,1] generating graphics... => 105
[4,2] generating graphics... => 81
[4,1,1] generating graphics... => 0
[3,3] generating graphics... => 30
[3,2,1] generating graphics... => 0
[3,1,1,1] generating graphics... => 0
[2,2,2] generating graphics... => 0
[2,2,1,1] generating graphics... => 0
[2,1,1,1,1] generating graphics... => 0
[1,1,1,1,1,1] generating graphics... => 0
[7] generating graphics... => 120
[6,1] generating graphics... => 160
[5,2] generating graphics... => 140
[5,1,1] generating graphics... => 0
[4,3] generating graphics... => 80
[4,2,1] generating graphics... => 0
[4,1,1,1] generating graphics... => 0
[3,3,1] generating graphics... => 0
[3,2,2] generating graphics... => 0
[3,2,1,1] generating graphics... => 0
[3,1,1,1,1] generating graphics... => 0
[2,2,2,1] generating graphics... => 0
[2,2,1,1,1] generating graphics... => 0
[2,1,1,1,1,1] generating graphics... => 0
[1,1,1,1,1,1,1] generating graphics... => 0
[8] generating graphics... => 165
[7,1] generating graphics... => 231
[6,2] generating graphics... => 220
[6,1,1] generating graphics... => 0
[5,3] generating graphics... => 154
[5,2,1] generating graphics... => 0
[5,1,1,1] generating graphics... => 0
[4,4] generating graphics... => 55
[4,3,1] generating graphics... => 0
[4,2,2] generating graphics... => 0
[4,2,1,1] generating graphics... => 0
[4,1,1,1,1] generating graphics... => 0
[3,3,2] generating graphics... => 0
[3,3,1,1] generating graphics... => 0
[3,2,2,1] generating graphics... => 0
[3,2,1,1,1] generating graphics... => 0
[3,1,1,1,1,1] generating graphics... => 0
[2,2,2,2] generating graphics... => 0
[2,2,2,1,1] generating graphics... => 0
[2,2,1,1,1,1] generating graphics... => 0
[2,1,1,1,1,1,1] generating graphics... => 0
[1,1,1,1,1,1,1,1] generating graphics... => 0
[9] generating graphics... => 220
[8,1] generating graphics... => 320
[7,2] generating graphics... => 324
[7,1,1] generating graphics... => 0
[6,3] generating graphics... => 256
[6,2,1] generating graphics... => 0
[6,1,1,1] generating graphics... => 0
[5,4] generating graphics... => 140
[5,3,1] generating graphics... => 0
[5,2,2] generating graphics... => 0
[5,2,1,1] generating graphics... => 0
[5,1,1,1,1] generating graphics... => 0
[4,4,1] generating graphics... => 0
[4,3,2] generating graphics... => 0
[4,3,1,1] generating graphics... => 0
[4,2,2,1] generating graphics... => 0
[4,2,1,1,1] generating graphics... => 0
[4,1,1,1,1,1] generating graphics... => 0
[3,3,3] generating graphics... => 0
[3,3,2,1] generating graphics... => 0
[3,3,1,1,1] generating graphics... => 0
[3,2,2,2] generating graphics... => 0
[3,2,2,1,1] generating graphics... => 0
[3,2,1,1,1,1] generating graphics... => 0
[3,1,1,1,1,1,1] generating graphics... => 0
[2,2,2,2,1] generating graphics... => 0
[2,2,2,1,1,1] generating graphics... => 0
[2,2,1,1,1,1,1] generating graphics... => 0
[2,1,1,1,1,1,1,1] generating graphics... => 0
[1,1,1,1,1,1,1,1,1] generating graphics... => 0
[10] generating graphics... => 286
[9,1] generating graphics... => 429
[8,2] generating graphics... => 455
[8,1,1] generating graphics... => 0
[7,3] generating graphics... => 390
[7,2,1] generating graphics... => 0
[7,1,1,1] generating graphics... => 0
[6,4] generating graphics... => 260
[6,3,1] generating graphics... => 0
[6,2,2] generating graphics... => 0
[6,2,1,1] generating graphics... => 0
[6,1,1,1,1] generating graphics... => 0
[5,5] generating graphics... => 91
[5,4,1] generating graphics... => 0
[5,3,2] generating graphics... => 0
[5,3,1,1] generating graphics... => 0
[5,2,2,1] generating graphics... => 0
[5,2,1,1,1] generating graphics... => 0
[5,1,1,1,1,1] generating graphics... => 0
[4,4,2] generating graphics... => 0
[4,4,1,1] generating graphics... => 0
[4,3,3] generating graphics... => 0
[4,3,2,1] generating graphics... => 0
[4,3,1,1,1] generating graphics... => 0
[4,2,2,2] generating graphics... => 0
[4,2,2,1,1] generating graphics... => 0
[4,2,1,1,1,1] generating graphics... => 0
[4,1,1,1,1,1,1] generating graphics... => 0
[3,3,3,1] generating graphics... => 0
[3,3,2,2] generating graphics... => 0
[3,3,2,1,1] generating graphics... => 0
[3,3,1,1,1,1] generating graphics... => 0
[3,2,2,2,1] generating graphics... => 0
[3,2,2,1,1,1] generating graphics... => 0
[3,2,1,1,1,1,1] generating graphics... => 0
[3,1,1,1,1,1,1,1] generating graphics... => 0
[2,2,2,2,2] generating graphics... => 0
[2,2,2,2,1,1] generating graphics... => 0
[2,2,2,1,1,1,1] generating graphics... => 0
[2,2,1,1,1,1,1,1] generating graphics... => 0
[2,1,1,1,1,1,1,1,1] generating graphics... => 0
[1,1,1,1,1,1,1,1,1,1] generating graphics... => 0
[11] generating graphics... => 364
[10,1] generating graphics... => 560
[9,2] generating graphics... => 616
[9,1,1] generating graphics... => 0
[8,3] generating graphics... => 560
[8,2,1] generating graphics... => 0
[8,1,1,1] generating graphics... => 0
[7,4] generating graphics... => 420
[7,3,1] generating graphics... => 0
[7,2,2] generating graphics... => 0
[7,2,1,1] generating graphics... => 0
[7,1,1,1,1] generating graphics... => 0
[6,5] generating graphics... => 224
[6,4,1] generating graphics... => 0
[6,3,2] generating graphics... => 0
[6,3,1,1] generating graphics... => 0
[6,2,2,1] generating graphics... => 0
[6,2,1,1,1] generating graphics... => 0
[6,1,1,1,1,1] generating graphics... => 0
[5,5,1] generating graphics... => 0
[5,4,2] generating graphics... => 0
[5,4,1,1] generating graphics... => 0
[5,3,3] generating graphics... => 0
[5,3,2,1] generating graphics... => 0
[5,3,1,1,1] generating graphics... => 0
[5,2,2,2] generating graphics... => 0
[5,2,2,1,1] generating graphics... => 0
[5,2,1,1,1,1] generating graphics... => 0
[5,1,1,1,1,1,1] generating graphics... => 0
[4,4,3] generating graphics... => 0
[4,4,2,1] generating graphics... => 0
[4,4,1,1,1] generating graphics... => 0
[4,3,3,1] generating graphics... => 0
[4,3,2,2] generating graphics... => 0
[4,3,2,1,1] generating graphics... => 0
[4,3,1,1,1,1] generating graphics... => 0
[4,2,2,2,1] generating graphics... => 0
[4,2,2,1,1,1] generating graphics... => 0
[4,2,1,1,1,1,1] generating graphics... => 0
[4,1,1,1,1,1,1,1] generating graphics... => 0
[3,3,3,2] generating graphics... => 0
[3,3,3,1,1] generating graphics... => 0
[3,3,2,2,1] generating graphics... => 0
[3,3,2,1,1,1] generating graphics... => 0
[3,3,1,1,1,1,1] generating graphics... => 0
[3,2,2,2,2] generating graphics... => 0
[3,2,2,2,1,1] generating graphics... => 0
[3,2,2,1,1,1,1] generating graphics... => 0
[3,2,1,1,1,1,1,1] generating graphics... => 0
[3,1,1,1,1,1,1,1,1] generating graphics... => 0
[2,2,2,2,2,1] generating graphics... => 0
[2,2,2,2,1,1,1] generating graphics... => 0
[2,2,2,1,1,1,1,1] generating graphics... => 0
[2,2,1,1,1,1,1,1,1] generating graphics... => 0
[2,1,1,1,1,1,1,1,1,1] generating graphics... => 0
[1,1,1,1,1,1,1,1,1,1,1] generating graphics... => 0
[12] generating graphics... => 455
[11,1] generating graphics... => 715
[10,2] generating graphics... => 810
[10,1,1] generating graphics... => 0
[9,3] generating graphics... => 770
[9,2,1] generating graphics... => 0
[9,1,1,1] generating graphics... => 0
[8,4] generating graphics... => 625
[8,3,1] generating graphics... => 0
[8,2,2] generating graphics... => 0
[8,2,1,1] generating graphics... => 0
[8,1,1,1,1] generating graphics... => 0
[7,5] generating graphics... => 405
[7,4,1] generating graphics... => 0
[7,3,2] generating graphics... => 0
[7,3,1,1] generating graphics... => 0
[7,2,2,1] generating graphics... => 0
[7,2,1,1,1] generating graphics... => 0
[7,1,1,1,1,1] generating graphics... => 0
[6,6] generating graphics... => 140
[6,5,1] generating graphics... => 0
[6,4,2] generating graphics... => 0
[6,4,1,1] generating graphics... => 0
[6,3,3] generating graphics... => 0
[6,3,2,1] generating graphics... => 0
[6,3,1,1,1] generating graphics... => 0
[6,2,2,2] generating graphics... => 0
[6,2,2,1,1] generating graphics... => 0
[6,2,1,1,1,1] generating graphics... => 0
[6,1,1,1,1,1,1] generating graphics... => 0
[5,5,2] generating graphics... => 0
[5,5,1,1] generating graphics... => 0
[5,4,3] generating graphics... => 0
[5,4,2,1] generating graphics... => 0
[5,4,1,1,1] generating graphics... => 0
[5,3,3,1] generating graphics... => 0
[5,3,2,2] generating graphics... => 0
[5,3,2,1,1] generating graphics... => 0
[5,3,1,1,1,1] generating graphics... => 0
[5,2,2,2,1] generating graphics... => 0
[5,2,2,1,1,1] generating graphics... => 0
[5,2,1,1,1,1,1] generating graphics... => 0
[5,1,1,1,1,1,1,1] generating graphics... => 0
[4,4,4] generating graphics... => 0
[4,4,3,1] generating graphics... => 0
[4,4,2,2] generating graphics... => 0
[4,4,2,1,1] generating graphics... => 0
[4,4,1,1,1,1] generating graphics... => 0
[4,3,3,2] generating graphics... => 0
[4,3,3,1,1] generating graphics... => 0
[4,3,2,2,1] generating graphics... => 0
[4,3,2,1,1,1] generating graphics... => 0
[4,3,1,1,1,1,1] generating graphics... => 0
[4,2,2,2,2] generating graphics... => 0
[4,2,2,2,1,1] generating graphics... => 0
[4,2,2,1,1,1,1] generating graphics... => 0
[4,2,1,1,1,1,1,1] generating graphics... => 0
[4,1,1,1,1,1,1,1,1] generating graphics... => 0
[3,3,3,3] generating graphics... => 0
[3,3,3,2,1] generating graphics... => 0
[3,3,3,1,1,1] generating graphics... => 0
[3,3,2,2,2] generating graphics... => 0
[3,3,2,2,1,1] generating graphics... => 0
[3,3,2,1,1,1,1] generating graphics... => 0
[3,3,1,1,1,1,1,1] generating graphics... => 0
[3,2,2,2,2,1] generating graphics... => 0
[3,2,2,2,1,1,1] generating graphics... => 0
[3,2,2,1,1,1,1,1] generating graphics... => 0
[3,2,1,1,1,1,1,1,1] generating graphics... => 0
[3,1,1,1,1,1,1,1,1,1] generating graphics... => 0
[2,2,2,2,2,2] generating graphics... => 0
[2,2,2,2,2,1,1] generating graphics... => 0
[2,2,2,2,1,1,1,1] generating graphics... => 0
[2,2,2,1,1,1,1,1,1] generating graphics... => 0
[2,2,1,1,1,1,1,1,1,1] generating graphics... => 0
[2,1,1,1,1,1,1,1,1,1,1] generating graphics... => 0
[1,1,1,1,1,1,1,1,1,1,1,1] generating graphics... => 0
click to show generating function       
Description
The dimension of the irreducible representation of Sp(4) labelled by an integer partition.
Consider the symplectic group $Sp(2n)$. Then the integer partition $(\mu_1,\dots,\mu_k)$ of length at most $n$ corresponds to the weight vector $(\mu_1-\mu_2,\dots,\mu_{k-2}-\mu_{k-1},\mu_n,0,\dots,0)$.
For example, the integer partition $(2)$ labels the symmetric square of the vector representation, whereas the integer partition $(1,1)$ labels the second fundamental representation.
Code
def statistic(mu):
    C = CartanType("C2")
    if len(mu) <= C.rank() or (C.type()=="A" and len(mu) <= C.rank()+1):
        w = [m1-m2 for m1,m2 in zip(mu, mu[1:])] + [mu[-1]] + [0]*(C.rank()-len(mu))
        return WeylDim(C, w)
    else:
        return 0
Created
Mar 21, 2017 at 08:29 by Martin Rubey
Updated
Mar 21, 2017 at 08:29 by Martin Rubey