

A272696


Coxeter number for the reflection group E_n.


1




OFFSET

3,1


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.


REFERENCES

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


LINKS



EXAMPLE

Starting with the CoxeterDynkin 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


CROSSREFS



KEYWORD

nonn,fini,full


AUTHOR



STATUS

approved



