cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Previous Showing 11-15 of 15 results.

A340523 Weight multiplicities for 248-dimensional irreducible representation of the Lie algebra E_8.

Original entry on oeis.org

1, 7, 35, 29, 111, 455, 1056, 1624, 645, 2296, 1584, 7504, 18081, 15959, 28441
Offset: 1

Views

Author

N. J. A. Sloane, Feb 08 2021

Keywords

Links

Crossrefs

Cf. A004009, A121732, A340522, A341289, A341290.

A341289 Weight multiplicities for 3875-dimensional irreducible representation of the Lie algebra E_8.

Original entry on oeis.org

1, 7, 6, 29, 133, 350, 552, 224, 826, 580, 2864, 7279, 6504, 12103
Offset: 2

Views

Author

N. J. A. Sloane, Feb 08 2021

Keywords

Links

Crossrefs

Cf. A004009, A121732, A340522, A340523, A341290.

A341290 Weight multiplicities for 30380-dimensional irreducible representation of the Lie algebra E_8.

Original entry on oeis.org

1, 1, 6, 34, 105, 174, 74, 275, 198, 1028, 2790, 2535, 4938
Offset: 3

Views

Author

N. J. A. Sloane, Feb 08 2021

Keywords

Links

Crossrefs

Cf. A004009, A121732, A340522, A340523, A341289.

A124680 Heights of irreducible representations of E_8.

Original entry on oeis.org

58, 92, 114, 136, 168, 182, 220, 270
Offset: 1

Views

Author

Roger L. Bagula, Dec 25 2005

Keywords

Examples

			The factored sequence, [2*29, 2^2*23, 2*3*19, 2^3*17, 2^3*3*7, 2*7*13, 2^2*5*11, 2*3^3*5], shows a close relationship to A005776. - _N. J. A. Sloane_, Dec 25 2006

References

  • R. N. Cahn, Semi-Simple Lie Algebras and Their Representations, Dover, NY, 2006, ISBN 0-486-44999-8, p. 139.

Crossrefs

Cf. A005776, A030650, A121732.

A263005 Dimensions of the simple Lie algebras over complex numbers (with repetitions), sorted nondecreasingly.

Original entry on oeis.org

3, 8, 10, 14, 15, 21, 21, 24, 28, 35, 36, 36, 45, 48, 55, 55, 57, 63, 66, 78, 78, 78, 80, 91, 99, 105, 105, 120, 120, 133, 136, 136, 143, 153, 168, 171, 171, 190, 195, 210, 210, 224, 231, 248, 253, 253, 255, 276, 288, 300, 300
Offset: 1

Views

Author

Wolfdieter Lang, Oct 23 2015

Keywords

Comments

This sequence gives the dimensions of the (compact) simple Lie algebras A_l, l >= 1, B_l, l >= 2, C_l >= 3, D_l, l >= 4, E_6, E_7, E_8, F_4 and G_2 which are l*(l+2), l*(2*l + 1), l*(2*l + 1), l*(2*l - 1), 78, 133, 248, 52 and 14, respectively. These are also the dimensions of the adjoint representations of these Lie algebras. For the l-ranges see the Humphreys reference, p. 58, and for the dimensions, e.g., the Samelson link, Theorem A, p. 74.
The dimension duplications occur for the B_l and C_l series for l >= 3.

References

  • E. Cartan, Sur la structure des groupes de transformation finis et continus. Thèse Paris 1894. Oeuvres Complètes, I,1, pp. 137-287, Paris 1952.
  • J. E. Humphreys, Introduction to Lie algebras and representation theory, Springer, 1972.

Links

  • W. Killing, Die Zusammensetzung der stetigen endlichen Transformationsgruppen, Mathematische Ann. I: 31 (1888) 252-290, II: 33 (1889) 1-48, III: 34 (1889) 57-122, IV: 36 (1890) 161-189: I, II, III, IV.
  • Hans Samelson, Notes on Lie Algebras.

Crossrefs

Cf. A104599, A121214, A121732, A121736, A121737, A121738, A121739, A121741.
Previous Showing 11-15 of 15 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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