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Identifier
Values
=>
Cc0002;cc-rep
[2]=>10 [1,1]=>5 [3]=>20 [2,1]=>16 [1,1,1]=>0 [4]=>35 [3,1]=>35 [2,2]=>14 [2,1,1]=>0 [1,1,1,1]=>0 [5]=>56 [4,1]=>64 [3,2]=>40 [3,1,1]=>0 [2,2,1]=>0 [2,1,1,1]=>0 [1,1,1,1,1]=>0 [6]=>84 [5,1]=>105 [4,2]=>81 [4,1,1]=>0 [3,3]=>30 [3,2,1]=>0 [3,1,1,1]=>0 [2,2,2]=>0 [2,2,1,1]=>0 [2,1,1,1,1]=>0 [1,1,1,1,1,1]=>0 [7]=>120 [6,1]=>160 [5,2]=>140 [5,1,1]=>0 [4,3]=>80 [4,2,1]=>0 [4,1,1,1]=>0 [3,3,1]=>0 [3,2,2]=>0 [3,2,1,1]=>0 [3,1,1,1,1]=>0 [2,2,2,1]=>0 [2,2,1,1,1]=>0 [2,1,1,1,1,1]=>0 [1,1,1,1,1,1,1]=>0 [8]=>165 [7,1]=>231 [6,2]=>220 [6,1,1]=>0 [5,3]=>154 [5,2,1]=>0 [5,1,1,1]=>0 [4,4]=>55 [4,3,1]=>0 [4,2,2]=>0 [4,2,1,1]=>0 [4,1,1,1,1]=>0 [3,3,2]=>0 [3,3,1,1]=>0 [3,2,2,1]=>0 [3,2,1,1,1]=>0 [3,1,1,1,1,1]=>0 [2,2,2,2]=>0 [2,2,2,1,1]=>0 [2,2,1,1,1,1]=>0 [2,1,1,1,1,1,1]=>0 [1,1,1,1,1,1,1,1]=>0 [9]=>220 [8,1]=>320 [7,2]=>324 [7,1,1]=>0 [6,3]=>256 [6,2,1]=>0 [6,1,1,1]=>0 [5,4]=>140 [5,3,1]=>0 [5,2,2]=>0 [5,2,1,1]=>0 [5,1,1,1,1]=>0 [4,4,1]=>0 [4,3,2]=>0 [4,3,1,1]=>0 [4,2,2,1]=>0 [4,2,1,1,1]=>0 [4,1,1,1,1,1]=>0 [3,3,3]=>0 [3,3,2,1]=>0 [3,3,1,1,1]=>0 [3,2,2,2]=>0 [3,2,2,1,1]=>0 [3,2,1,1,1,1]=>0 [3,1,1,1,1,1,1]=>0 [2,2,2,2,1]=>0 [2,2,2,1,1,1]=>0 [2,2,1,1,1,1,1]=>0 [2,1,1,1,1,1,1,1]=>0 [1,1,1,1,1,1,1,1,1]=>0 [10]=>286 [9,1]=>429 [8,2]=>455 [8,1,1]=>0 [7,3]=>390 [7,2,1]=>0 [7,1,1,1]=>0 [6,4]=>260 [6,3,1]=>0 [6,2,2]=>0 [6,2,1,1]=>0 [6,1,1,1,1]=>0 [5,5]=>91 [5,4,1]=>0 [5,3,2]=>0 [5,3,1,1]=>0 [5,2,2,1]=>0 [5,2,1,1,1]=>0 [5,1,1,1,1,1]=>0 [4,4,2]=>0 [4,4,1,1]=>0 [4,3,3]=>0 [4,3,2,1]=>0 [4,3,1,1,1]=>0 [4,2,2,2]=>0 [4,2,2,1,1]=>0 [4,2,1,1,1,1]=>0 [4,1,1,1,1,1,1]=>0 [3,3,3,1]=>0 [3,3,2,2]=>0 [3,3,2,1,1]=>0 [3,3,1,1,1,1]=>0 [3,2,2,2,1]=>0 [3,2,2,1,1,1]=>0 [3,2,1,1,1,1,1]=>0 [3,1,1,1,1,1,1,1]=>0 [2,2,2,2,2]=>0 [2,2,2,2,1,1]=>0 [2,2,2,1,1,1,1]=>0 [2,2,1,1,1,1,1,1]=>0 [2,1,1,1,1,1,1,1,1]=>0 [1,1,1,1,1,1,1,1,1,1]=>0 [11]=>364 [10,1]=>560 [9,2]=>616 [9,1,1]=>0 [8,3]=>560 [8,2,1]=>0 [8,1,1,1]=>0 [7,4]=>420 [7,3,1]=>0 [7,2,2]=>0 [7,2,1,1]=>0 [7,1,1,1,1]=>0 [6,5]=>224 [6,4,1]=>0 [6,3,2]=>0 [6,3,1,1]=>0 [6,2,2,1]=>0 [6,2,1,1,1]=>0 [6,1,1,1,1,1]=>0 [5,5,1]=>0 [5,4,2]=>0 [5,4,1,1]=>0 [5,3,3]=>0 [5,3,2,1]=>0 [5,3,1,1,1]=>0 [5,2,2,2]=>0 [5,2,2,1,1]=>0 [5,2,1,1,1,1]=>0 [5,1,1,1,1,1,1]=>0 [4,4,3]=>0 [4,4,2,1]=>0 [4,4,1,1,1]=>0 [4,3,3,1]=>0 [4,3,2,2]=>0 [4,3,2,1,1]=>0 [4,3,1,1,1,1]=>0 [4,2,2,2,1]=>0 [4,2,2,1,1,1]=>0 [4,2,1,1,1,1,1]=>0 [4,1,1,1,1,1,1,1]=>0 [3,3,3,2]=>0 [3,3,3,1,1]=>0 [3,3,2,2,1]=>0 [3,3,2,1,1,1]=>0 [3,3,1,1,1,1,1]=>0 [3,2,2,2,2]=>0 [3,2,2,2,1,1]=>0 [3,2,2,1,1,1,1]=>0 [3,2,1,1,1,1,1,1]=>0 [3,1,1,1,1,1,1,1,1]=>0 [2,2,2,2,2,1]=>0 [2,2,2,2,1,1,1]=>0 [2,2,2,1,1,1,1,1]=>0 [2,2,1,1,1,1,1,1,1]=>0 [2,1,1,1,1,1,1,1,1,1]=>0 [1,1,1,1,1,1,1,1,1,1,1]=>0 [12]=>455 [11,1]=>715 [10,2]=>810 [10,1,1]=>0 [9,3]=>770 [9,2,1]=>0 [9,1,1,1]=>0 [8,4]=>625 [8,3,1]=>0 [8,2,2]=>0 [8,2,1,1]=>0 [8,1,1,1,1]=>0 [7,5]=>405 [7,4,1]=>0 [7,3,2]=>0 [7,3,1,1]=>0 [7,2,2,1]=>0 [7,2,1,1,1]=>0 [7,1,1,1,1,1]=>0 [6,6]=>140 [6,5,1]=>0 [6,4,2]=>0 [6,4,1,1]=>0 [6,3,3]=>0 [6,3,2,1]=>0 [6,3,1,1,1]=>0 [6,2,2,2]=>0 [6,2,2,1,1]=>0 [6,2,1,1,1,1]=>0 [6,1,1,1,1,1,1]=>0 [5,5,2]=>0 [5,5,1,1]=>0 [5,4,3]=>0 [5,4,2,1]=>0 [5,4,1,1,1]=>0 [5,3,3,1]=>0 [5,3,2,2]=>0 [5,3,2,1,1]=>0 [5,3,1,1,1,1]=>0 [5,2,2,2,1]=>0 [5,2,2,1,1,1]=>0 [5,2,1,1,1,1,1]=>0 [5,1,1,1,1,1,1,1]=>0 [4,4,4]=>0 [4,4,3,1]=>0 [4,4,2,2]=>0 [4,4,2,1,1]=>0 [4,4,1,1,1,1]=>0 [4,3,3,2]=>0 [4,3,3,1,1]=>0 [4,3,2,2,1]=>0 [4,3,2,1,1,1]=>0 [4,3,1,1,1,1,1]=>0 [4,2,2,2,2]=>0 [4,2,2,2,1,1]=>0 [4,2,2,1,1,1,1]=>0 [4,2,1,1,1,1,1,1]=>0 [4,1,1,1,1,1,1,1,1]=>0 [3,3,3,3]=>0 [3,3,3,2,1]=>0 [3,3,3,1,1,1]=>0 [3,3,2,2,2]=>0 [3,3,2,2,1,1]=>0 [3,3,2,1,1,1,1]=>0 [3,3,1,1,1,1,1,1]=>0 [3,2,2,2,2,1]=>0 [3,2,2,2,1,1,1]=>0 [3,2,2,1,1,1,1,1]=>0 [3,2,1,1,1,1,1,1,1]=>0 [3,1,1,1,1,1,1,1,1,1]=>0 [2,2,2,2,2,2]=>0 [2,2,2,2,2,1,1]=>0 [2,2,2,2,1,1,1,1]=>0 [2,2,2,1,1,1,1,1,1]=>0 [2,2,1,1,1,1,1,1,1,1]=>0 [2,1,1,1,1,1,1,1,1,1,1]=>0 [1,1,1,1,1,1,1,1,1,1,1,1]=>0
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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