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.

Showing 1-2 of 2 results.

A272696 Coxeter number for the reflection group E_n.

Original entry on oeis.org

6, 5, 8, 12, 18, 30
Offset: 3

Views

Author

Curtis T. McMullen, May 04 2016

Keywords

Comments

A good definition of E_n is to take (-3,1,...,1)^perp in Z^(1,n) (and change the sign). This is the correct definition when one relates E_n to the blowup of P^2 at n points, and gives the sequence E_8, E_7, E_6, D_5, A_4, A_2 X A_1.
For n>8, the Coxeter number is infinity.

Examples

			Starting with the Coxeter-Dynkin diagram for E_8, one repeatedly chops off nodes from one end, getting the sequence E_8, E_7, E_6, D_5, A_4, A_2 X A_1, whose Coxeter numbers are 30, 18, 12, 8, 5, 3 X 2=6. - _N. J. A. Sloane_, May 05 2016

References

  • J. E. Humphreys, Reflection Groups and Coxeter Groups, Cambridge, 1990. See Table 3.2, page 80.

Links

Crossrefs

Cf. A272764.

A334597 Dimensions of the finite-dimensional Lie algebras of type E_n (n=3,...,8).

Original entry on oeis.org

11, 24, 45, 78, 133, 248
Offset: 3

Views

Author

Bart Vlaar, May 07 2020

Keywords

Comments

E_3 = A_1 A_2, E_4 = A_4, E_5 = D_5.

References

  • R. Carter, Lie Algebras of Finite and Affine Type, Cambridge University Press, 2005, 561-609.

Links

Crossrefs

The last three terms are the last three terms of A113907.

Formula

For n>3, a(n) = 2*A272764(n) + n (for n=3 the Lie algebra is not simple).
Showing 1-2 of 2 results.

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

Content is available under The OEIS End-User License Agreement.