| SL(2,ℝ)SL(2,\mathbb{R}) | 1 |
SL
(
2
,
ℤ
)
SL(2,\mathbb{Z})
S-duality | D=10 type IIB supergravity | |
| SL(2,ℝ)×(2,\mathbb{R}) \times O(1,1) | ℤ 2\mathbb{Z}_2 |
SL
(
2
,
ℤ
)
SL(2,\mathbb{Z})
×ℤ 2\times \mathbb{Z}_2 | D=9 supergravity | |
| SU(3)×\times SU(2) | SL(3,ℝ)×SL(2,ℝ)(3,\mathbb{R}) \times SL(2,\mathbb{R}) | O(2,2;ℤ)O(2,2;\mathbb{Z}) | SL(3,ℤ)×SL(2,ℤ)SL(3,\mathbb{Z})\times SL(2,\mathbb{Z}) | D=8 supergravity | |
| SU(5) | SL(5,ℝ)SL(5,\mathbb{R}) | O(3,3;ℤ)O(3,3;\mathbb{Z}) | SL(5,ℤ)SL(5,\mathbb{Z}) | D=7 supergravity | |
| Spin(10) | Spin(5,5)Spin(5,5) | O(4,4;ℤ)O(4,4;\mathbb{Z}) | O(5,5,ℤ)O(5,5,\mathbb{Z}) | D=6 supergravity | |
| E₆ | E 6(6)E_{6(6)} | O(5,5;ℤ)O(5,5;\mathbb{Z}) | E 6(6)(ℤ)E_{6(6)}(\mathbb{Z}) | D=5 supergravity | |
| E₇ | E 7(7)E_{7(7)} | O(6,6;ℤ)O(6,6;\mathbb{Z}) | E 7(7)(ℤ)E_{7(7)}(\mathbb{Z}) | D=4 supergravity | |
| E₈ | E 8(8)E_{8(8)} | O(7,7;ℤ)O(7,7;\mathbb{Z}) | E 8(8)(ℤ)E_{8(8)}(\mathbb{Z}) | D=3 supergravity | |
| E₉ | E 9(9)E_{9(9)} | O(8,8;ℤ)O(8,8;\mathbb{Z}) | E 9(9)(ℤ)E_{9(9)}(\mathbb{Z}) | D=2 supergravity | E₈-equivariant elliptic cohomology |
| E₁₀ | E 10(10)E_{10(10)} | O(9,9;ℤ)O(9,9;\mathbb{Z}) | E 10(10)(ℤ)E_{10(10)}(\mathbb{Z}) | | |
| E₁₁ | E 11(11)E_{11(11)} | O(10,10;ℤ)O(10,10;\mathbb{Z}) | E 11(11)(ℤ)E_{11(11)}(\mathbb{Z}) | | |