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Identifier
Values
=>
Cc0002;cc-rep
[2]=>21 [1,1]=>14 [3]=>56 [2,1]=>64 [1,1,1]=>14 [4]=>126 [3,1]=>189 [2,2]=>90 [2,1,1]=>70 [1,1,1,1]=>0 [5]=>252 [4,1]=>448 [3,2]=>350 [3,1,1]=>216 [2,2,1]=>126 [2,1,1,1]=>0 [1,1,1,1,1]=>0 [6]=>462 [5,1]=>924 [4,2]=>924 [4,1,1]=>525 [3,3]=>385 [3,2,1]=>512 [3,1,1,1]=>0 [2,2,2]=>84 [2,2,1,1]=>0 [2,1,1,1,1]=>0 [1,1,1,1,1,1]=>0 [7]=>792 [6,1]=>1728 [5,2]=>2016 [5,1,1]=>1100 [4,3]=>1344 [4,2,1]=>1386 [4,1,1,1]=>0 [3,3,1]=>616 [3,2,2]=>378 [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]=>1287 [7,1]=>3003 [6,2]=>3900 [6,1,1]=>2079 [5,3]=>3276 [5,2,1]=>3072 [5,1,1,1]=>0 [4,4]=>1274 [4,3,1]=>2205 [4,2,2]=>1078 [4,2,1,1]=>0 [4,1,1,1,1]=>0 [3,3,2]=>594 [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]=>2002 [8,1]=>4928 [7,2]=>6930 [7,1,1]=>3640 [6,3]=>6720 [6,2,1]=>6006 [6,1,1,1]=>0 [5,4]=>4116 [5,3,1]=>5460 [5,2,2]=>2464 [5,2,1,1]=>0 [5,1,1,1,1]=>0 [4,4,1]=>2184 [4,3,2]=>2240 [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]=>330 [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]=>3003 [9,1]=>7722 [8,2]=>11550 [8,1,1]=>6006 [7,3]=>12375 [7,2,1]=>10752 [7,1,1,1]=>0 [6,4]=>9450 [6,3,1]=>11319 [6,2,2]=>4914 [6,2,1,1]=>0 [6,1,1,1,1]=>0 [5,5]=>3528 [5,4,1]=>7168 [5,3,2]=>5720 [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]=>2457 [4,4,1,1]=>0 [4,3,3]=>1386 [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]=>4368 [10,1]=>11648 [9,2]=>18304 [9,1,1]=>9450 [8,3]=>21120 [8,2,1]=>18018 [8,1,1,1]=>0 [7,4]=>18480 [7,3,1]=>21000 [7,2,2]=>8918 [7,2,1,1]=>0 [7,1,1,1,1]=>0 [6,5]=>10752 [6,4,1]=>16632 [6,3,2]=>12096 [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]=>6300 [5,4,2]=>8316 [5,4,1,1]=>0 [5,3,3]=>3744 [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]=>2002 [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]=>6188 [11,1]=>17017 [10,2]=>27846 [10,1,1]=>14300 [9,3]=>34034 [9,2,1]=>28672 [9,1,1,1]=>0 [8,4]=>32725 [8,3,1]=>36036 [8,2,2]=>15092 [8,2,1,1]=>0 [8,1,1,1,1]=>0 [7,5]=>23562 [7,4,1]=>32768 [7,3,2]=>22750 [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]=>8568 [6,5,1]=>19404 [6,4,2]=>19683 [6,4,1,1]=>0 [6,3,3]=>8190 [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]=>7700 [5,5,1,1]=>0 [5,4,3]=>7168 [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]=>1001 [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(6) 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("C3")
    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 08:32 by Martin Rubey
Updated
Mar 21, 2017 at 08:32 by Martin Rubey