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Algebra
CartanMatrix
DecomposeIrrep
DecomposeProduct
DimName
Dim
HighestRoot
Index
Irrep
IrrepPlus
LaTeXForm
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PositiveRoots
ProductAlgebra
ProductIrrep
RootSystem
WeightSystem
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BranchingRules
IrrepProperties
TensorProducts

Tables of Branching Rules

following R. Slansky, “Group Theory for Unified Model Building”, Phys.Rept. 79 (1981) 1 - 128

Initialization


SU(N)

In[]:=

BranchingRulesTable[SU2,{U1},MaxDim->29,MaxDynkinDigit->28]

Total time: 0.3s

Out[]=

Table1: SU(2) Branching Rules

SU(2)	→	U(1)
2	=	(1)+(-1)
3	=	(2)+(0)+(-2)
4	=	(3)+(1)+(-1)+(-3)
5	=	(4)+(2)+(0)+(-2)+(-4)
6	=	(5)+(3)+(1)+(-1)+(-3)+(-5)
7	=	(6)+(4)+(2)+(0)+(-2)+(-4)+(-6)
8	=	(7)+(5)+(3)+(1)+(-1)+(-3)+(-5)+(-7)
9	=	(8)+(6)+(4)+(2)+(0)+(-2)+(-4)+(-6)+(-8)
10	=	(9)+(7)+(5)+(3)+(1)+(-1)+(-3)+(-5)+(-7)+(-9)
11	=	(10)+(8)+(6)+(4)+(2)+(0)+(-2)+(-4)+(-6)+(-8)+(-10)
12	=	(11)+(9)+(7)+(5)+(3)+(1)+(-1)+(-3)+(-5)+(-7)+(-9)+(-11)
13	=	(12)+(10)+(8)+(6)+(4)+(2)+(0)+(-2)+(-4)+(-6)+(-8)+(-10)+(-12)
14	=	(13)+(11)+(9)+(7)+(5)+(3)+(1)+(-1)+(-3)+(-5)+(-7)+(-9)+(-11)+(-13)
15	=	(14)+(12)+(10)+(8)+(6)+(4)+(2)+(0)+(-2)+(-4)+(-6)+(-8)+(-10)+(-12)+(-14)
16	=	(15)+(13)+(11)+(9)+(7)+(5)+(3)+(1)+(-1)+(-3)+(-5)+(-7)+(-9)+(-11)+(-13)+(-15)
17	=	(16)+(14)+(12)+(10)+(8)+(6)+(4)+(2)+(0)+(-2)+(-4)+(-6)+(-8)+(-10)+(-12)+(-14)+(-16)
18	=	(17)+(15)+(13)+(11)+(9)+(7)+(5)+(3)+(1)+(-1)+(-3)+(-5)+(-7)+(-9)+(-11)+(-13)+(-15)+(-17)
19	=	(18)+(16)+(14)+(12)+(10)+(8)+(6)+(4)+(2)+(0)+(-2)+(-4)+(-6)+(-8)+(-10)+(-12)+(-14)+(-16)+(-18)
20	=	(19)+(17)+(15)+(13)+(11)+(9)+(7)+(5)+(3)+(1)+(-1)+(-3)+(-5)+(-7)+(-9)+(-11)+(-13)+(-15)+(-17)+(-19)
21	=	(20)+(18)+(16)+(14)+(12)+(10)+(8)+(6)+(4)+(2)+(0)+(-2)+(-4)+(-6)+(-8)+(-10)+(-12)+(-14)+(-16)+(-18)+(-20)
22	=	(21)+(19)+(17)+(15)+(13)+(11)+(9)+(7)+(5)+(3)+(1)+(-1)+(-3)+(-5)+(-7)+(-9)+(-11)+(-13)+(-15)+(-17)+(-19)+(-21)
23	=	(22)+(20)+(18)+(16)+(14)+(12)+(10)+(8)+(6)+(4)+(2)+(0)+(-2)+(-4)+(-6)+(-8)+(-10)+(-12)+(-14)+(-16)+(-18)+(-20)+(-22)
24	=	(23)+(21)+(19)+(17)+(15)+(13)+(11)+(9)+(7)+(5)+(3)+(1)+(-1)+(-3)+(-5)+(-7)+(-9)+(-11)+(-13)+(-15)+(-17)+(-19)+(-21)+(-23)
25	=	(24)+(22)+(20)+(18)+(16)+(14)+(12)+(10)+(8)+(6)+(4)+(2)+(0)+(-2)+(-4)+(-6)+(-8)+(-10)+(-12)+(-14)+(-16)+(-18)+(-20)+(-22)+(-24)
26	=	(25)+(23)+(21)+(19)+(17)+(15)+(13)+(11)+(9)+(7)+(5)+(3)+(1)+(-1)+(-3)+(-5)+(-7)+(-9)+(-11)+(-13)+(-15)+(-17)+(-19)+(-21)+(-23)+(-25)
27	=	(26)+(24)+(22)+(20)+(18)+(16)+(14)+(12)+(10)+(8)+(6)+(4)+(2)+(0)+(-2)+(-4)+(-6)+(-8)+(-10)+(-12)+(-14)+(-16)+(-18)+(-20)+(-22)+(-24)+(-26)
28	=	(27)+(25)+(23)+(21)+(19)+(17)+(15)+(13)+(11)+(9)+(7)+(5)+(3)+(1)+(-1)+(-3)+(-5)+(-7)+(-9)+(-11)+(-13)+(-15)+(-17)+(-19)+(-21)+(-23)+(-25)+(-27)
29	=	(28)+(26)+(24)+(22)+(20)+(18)+(16)+(14)+(12)+(10)+(8)+(6)+(4)+(2)+(0)+(-2)+(-4)+(-6)+(-8)+(-10)+(-12)+(-14)+(-16)+(-18)+(-20)+(-22)+(-24)+(-26)+(-28)

In[]:=

BranchingRulesTable[SU3,{ProductAlgebra[SU2,U1],SU2},MaxDim->132,MaxDynkinDigit->15]

Total time: 1.8s

Out[]=

In[]:=

BranchingRulesTable[SU4,{ProductAlgebra[SU3,U1],ProductAlgebra[SU2,SU2,U1],Sp4,ProductAlgebra[SU2,SU2]},MaxDim->84,MaxDynkinDigit->7]

Total time: 0.9s

Out[]=

In[]:=

BranchingRulesTable[SU5,{ProductAlgebra[SU4,U1],ProductAlgebra[SU3,SU2,U1],Sp4},MaxDim->210,MaxDynkinDigit->6]

Total time: 1.8s

Out[]=

In[]:=

BranchingRulesTable[SU6,{ProductAlgebra[SU5,U1],ProductAlgebra[SU4,SU2,U1],ProductAlgebra[SU3,SU3,U1],SU3,SU4,Sp6,ProductAlgebra[SU3,SU2]},MaxDim->384,MaxDynkinDigit->5]

Total time: 5.3s

Out[]=

In[]:=

BranchingRulesTable[SU7,{ProductAlgebra[SU6,U1],ProductAlgebra[SU5,SU2,U1],ProductAlgebra[SU4,SU3,U1],SO7},MaxDim->840,MaxDynkinDigit->5]

Total time: 11.1s

Out[]=

In[]:=

BranchingRulesTable[SU8,{ProductAlgebra[SU7,U1],ProductAlgebra[SU6,SU2,U1],ProductAlgebra[SU5,SU3,U1],ProductAlgebra[SU4,SU4,U1],SO8,Sp8,ProductAlgebra[SU4,SU2]},MaxDim->945,MaxDynkinDigit->5]

Total time: 30.7s

Out[]=

In[]:=

BranchingRulesTable[SU9,{ProductAlgebra[SU8,U1],ProductAlgebra[SU7,SU2,U1],ProductAlgebra[SU6,SU3,U1],ProductAlgebra[SU5,SU4,U1],SO9,ProductAlgebra[SU3,SU3]},MaxDim->1215,MaxDynkinDigit->4]

Total time: 46.3s

Out[]=

In[]:=

BranchingRulesTable[SU10,{ProductAlgebra[SU9,U1],ProductAlgebra[SU8,SU2,U1],ProductAlgebra[SU7,SU3,U1],ProductAlgebra[SU6,SU4,U1],ProductAlgebra[SU5,SU5,U1],SU3,SU4,SU5,SO10,Sp10,ProductAlgebra[SU5,SU2]},MaxDim->1848,MaxDynkinDigit->4]

Total time: 216.0s

Out[]=

In[]:=

BranchingRulesTable[SU11,{ProductAlgebra[SU10,U1],ProductAlgebra[SU9,SU2,U1],ProductAlgebra[SU8,SU3,U1],ProductAlgebra[SU7,SU4,U1],ProductAlgebra[SU6,SU5,U1],SO11},MaxDim->1210,MaxDynkinDigit->3]

Total time: 111.0s

Out[]=

In[]:=

BranchingRulesTable[SU12,{ProductAlgebra[SU11,U1],ProductAlgebra[SU10,SU2,U1],ProductAlgebra[SU9,SU3,U1],ProductAlgebra[SU7,SU5,U1],ProductAlgebra[SU6,SU6,U1],SO12,Sp12,ProductAlgebra[SU6,SU2],ProductAlgebra[SU4,SU3]},MaxDim->1800,MaxDynkinDigit->3]

Total time: 479.0s

Out[]=

In[]:=

BranchingRulesTable[SU13,{ProductAlgebra[SU12,U1],ProductAlgebra[SU11,SU2,U1],ProductAlgebra[SU10,SU3,U1],ProductAlgebra[SU9,SU4,U1],ProductAlgebra[SU8,SU5,U1],ProductAlgebra[SU7,SU6,U1],SO13},MaxDynkinDigit->3,MaxDim->1170]

Total time: 2230.0s

Out[]=

In[]:=

BranchingRulesTable[SU14,{ProductAlgebra[SU13,U1],ProductAlgebra[SU12,SU2,U1],ProductAlgebra[SU11,SU3,U1],ProductAlgebra[SU10,SU4,U1],ProductAlgebra[SU9,SU5,U1],ProductAlgebra[SU8,SU6,U1],ProductAlgebra[SU7,SU7,U1],SO14,Sp14,ProductAlgebra[SU7,SU2]},MaxDynkinDigit->2,MaxDim->910]

Total time: 251.0s

Out[]=

In[]:=

BranchingRulesTable[SU15,{ProductAlgebra[SU14,U1],ProductAlgebra[SU13,SU2,U1],ProductAlgebra[SU12,SU3,U1],ProductAlgebra[SU11,SU4,U1],ProductAlgebra[SU10,SU5,U1],ProductAlgebra[SU9,SU6,U1],ProductAlgebra[SU8,SU7,U1],SO15,ProductAlgebra[SU5,SU3],SU5,SU6},MaxDynkinDigit->2,MaxDim->1560]

Total time: 862.0s

Out[]=

In[]:=

BranchingRulesTable[SU15,{SU3},MaxDynkinDigit->2,MaxDim->1560]

Total time: 4.3s

Out[]=

Table15: SU(15) Branching Rules

SU(15)	→	SU(3)
15	=	15
105	=	3 + 15 + 21 + 24 + 42
120	=	6+ 15 + ′ 15 + 24 + 60
224	=	2(8)+10+ 10 +2(27)+35+ 35 +64
455	=	1+8+2(10)+ 10 +3(27)+28+ 28 +35+ 35 +2(64)+81
1120	=	4(8)+2(10)+2( 10 )+5(27)+28+4(35)+3( 35 )+3(64)+80+2(81)+ 81 +125
1365	=	3( 6 )+4(15)+3( ′ 15 )+21+4(24)+4(42)+3(48)+4(60)+63+2(90)+2(105)+120
1560	=	2(3)+4( 6 )+6(15)+4( ′ 15 )+2(21)+6(24)+6(42)+3(48)+4(60)+63+3(90)+105+120

SU(15)	→	SU(3)
15	=	′ 15
105	=	42 + 63
120	=	′ 15 + 45 + 60
224	=	8+27+64+125
455	=	10+ 10 +55+64+81+ 81 +154
1120	=	8+27+35+ 35 +64+80+81+ 81 +2(125)+143+154+162
1365	=	15+24+36+42+48+60+63+90+105+120+165+192+195+210
1560	=	2(15)+ ′ 15 +21+24+2(42)+2(48)+60+63+2(90)+105+120+132+165+192+273

In[]:=

BranchingRulesTable[SU16,{ProductAlgebra[SU15,U1],ProductAlgebra[SU14,SU2,U1],ProductAlgebra[SU13,SU3,U1],ProductAlgebra[SU12,SU4,U1],ProductAlgebra[SU11,SU5,U1],ProductAlgebra[SU10,SU6,U1],ProductAlgebra[SU9,SU7,U1],ProductAlgebra[SU8,SU8,U1],SO16,Sp16,SO10,ProductAlgebra[SU8,SU2],ProductAlgebra[SU4,SU4]},MaxDynkinDigit->2,MaxDim->560]

Total time: 2850.0s

Out[]=

Wolfram Language Paclet Repository

Tables of Branching Rules

Initialization


SU(N)

SO(N)

Sp(n)

Exceptional Algebras

Tables of Branching Rules

Initialization

SU(N)

SO(N)

Sp(n)

Exceptional Algebras

Initialization
