Bruce Westbury has authored 10 sequences.
A251594
Dimension of space of invariant tensors in 2n-th tensor power of third fundamental representation of Sp(8).
Original entry on oeis.org
1, 1, 7, 240, 21720, 3371661, 753384764, 221280081152, 8057098267140, 34901583348508312, 17450751376913065040, 9843352171270598267648, 6153355867118768196316096, 4203420758907186950461719325, 3102284883642894954937435310820
Offset: 0
-
p_tensor(2*n,[0,0,1,0],C4)|[0,0,0,0]
A251598
Dimension of space of invariant tensors in 2n-th tensor power of natural representation of Sp(8).
Original entry on oeis.org
1, 1, 3, 15, 105, 944, 10340, 133055, 1958060, 32279090, 586453658, 11589971918, 246518371679, 5594169454700, 134456679614850, 3402014360391645, 90146180439817440, 2490533922180210720, 71468389947184389600, 2123114263550335500000
Offset: 0
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p_tensor(2*n,[1,0,0,0],C4)|[0,0,0,0]
A251593
Dimension of space of invariant tensors in n-th tensor power of second fundamental representation of Sp(8).
Original entry on oeis.org
1, 0, 1, 1, 6, 21, 120, 702, 4851, 36549, 302031, 2687435, 25561745, 257747493, 2738202129, 30482602101, 353982846285, 427126636983, 53371267903029, 688581489582657, 9149097089801836, 124906922737719625, 1748648316615176130
Offset: 0
-
p_tensor(n,[0,1,0,0],C4)|[0,0,0,0]
A251596
Dimension of space of invariant tensors in n-th tensor power of fourth fundamental representation of Sp(8).
Original entry on oeis.org
1, 0, 1, 0, 5, 1, 70, 106, 2380, 12398, 184359, 1830820, 25990371, 348029255, 531547931, 83340599734, 1395460803100, 24298184539132, 442299791441900, 8348538362127894, 163180897579795284
Offset: 0
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p_tensor(n,[0,0,0,1],C4)|[0,0,0,0]
A251591
Dimension of space of invariant tensors in 2n-th tensor power of the third fundamental representation of Sp(6).
Original entry on oeis.org
1, 1, 4, 35, 560, 14973, 589743, 30078048, 1824041570, 125400975830, 9507019477382, 78070828079199, 68560287232877740, 6376178095301876005, 623169409884847073730, 636070059202675270255520, 6745818886029778590765570, 740194253157571009569356970
Offset: 0
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p_tensor(2*n,[0,0,1],C3)|[0,0,0]
A227292
Dimension of space of invariant tensors in the n-th tensor power of the adjoint representation of G2.
Original entry on oeis.org
1, 0, 1, 1, 5, 16, 80, 436, 2786, 19538, 147771, 1182095, 9890463, 85866068, 769212600, 7080642324, 66754295740, 642857161008, 6309892895338, 6300760829973, 639049976047882, 6574281878157350, 68519019810831408, 722711344283052608, 7707346411412142258, 83037096707432139882
Offset: 0
For n=0 we have the trivial representation for n=2 we have the Killing form.
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p_tensor(n,[0,1],G2)|[0,0]
A179663
The dimension of the space of invariant tensors in the n-th tensor power of the adjoint representation of the exceptional Lie algebra E8.
Original entry on oeis.org
1, 0, 1, 1, 5, 16, 79, 421, 2674, 19244, 156612, 1423028, 14320350, 158390872, 1912977222, 25083283995, 355246037162, 5409471180024, 88200546561838, 1534120589972637, 28369229081383675, 556021169447494656, 11517512836906556032, 251487262264563372960
Offset: 0
The n-th tensor power is the trivial representation for n=0 and is the adjoint representation for n=1. For n=2 every invariant tensor is a scalar multiple of a Killing form.
A179683
The dimension of the space of invariant tensors in the n-th tensor power of the adjoint representation of the exceptional Lie algebra E7.
Original entry on oeis.org
1, 0, 1, 1, 5, 16, 80, 436, 2877, 21828, 189877, 1865175, 20468437, 248376198, 3303397123, 47785692843, 746841034620, 12538089887528, 224955746518560, 4294093811333388, 86859002770470072, 1855099612560598420, 41698660497526383757
Offset: 0
The n-th tensor power is the trivial representation for n=0 and is the adjoint representation for n=1. For n=2 every invariant tensor is a scalar multiple of a Killing form.
A179684
The dimension of the space of invariant tensors in the n-th tensor power of the adjoint representation of the exceptional Lie algebra E6.
Original entry on oeis.org
1, 0, 1, 1, 5, 17, 90, 542, 3962, 33554, 324489, 3520885, 42300709, 556530474, 7945317484, 122145525208, 2008827010000, 35143981009968
Offset: 0
The n-th tensor power is the trivial representation for n=0 and is the adjoint representation for n=1. For n=2 every invariant tensor is a scalar multiple of a Killing form.
A179685
The dimension of the space of invariant tensors in the n-th tensor power of the adjoint representation of the exceptional Lie algebra F4.
Original entry on oeis.org
1, 0, 1, 1, 5, 16, 80, 436, 2891, 22248, 198774, 2029140, 23310386, 296407466, 4109654354, 61348443380, 976111067870, 16423368282336, 290404344321126, 5370042566624118, 103427555919931446
Offset: 0
The n-th tensor power is the trivial representation for n=0 and is the adjoint representation for n=1. For n=2 every invariant tensor is a scalar multiple of a Killing form.
- Jacob L. Bourjaily, Michael Plesser, and Cristian Vergu, The Many Colours of Amplitudes, arXiv:2412.21189 [hep-th], 2024. See p. 53.
- Scott Morrison, Noah Snyder, and Dylan P. Thurston, Towards the quantum exceptional series, arXiv:2402.03637 [math.QA], 2024. See p. 38.
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