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.
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
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