This site is supported by donations to The OEIS Foundation.



Annual Appeal: Today, Nov 11 2014, is the 4th anniversary of the launch of the new OEIS web site. 70,000 sequences have been added in these four years, all edited by volunteers. Please make a donation (tax deductible in the US) to help keep the OEIS running.

(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A121732 Dimensions of the irreducible representations of the simple Lie algebra of type E8 over the complex numbers, listed in increasing order. 11
1, 248, 3875, 27000, 30380, 147250, 779247, 1763125, 2450240, 4096000, 4881384, 6696000, 26411008, 70680000, 76271625, 79143000, 146325270, 203205000, 281545875, 301694976, 344452500, 820260000, 1094951000, 2172667860 (list; graph; refs; listen; history; text; internal format)



We include "1" for the 1-dimensional trivial representation and we list each dimension once, ignoring the possibility that inequivalent representations may have the same dimension.

Inequivalent representations can have the same dimension. For example, the highest weights 10100000 and 10000011 (with fundamental weights numbered as in Bourbaki) both correspond to irreducible representations of dimension 8634368000.


J. E. Humphreys, Introduction to Lie algebras and representation theory, Springer, 1997.


Table of n, a(n) for n=1..24.

Skip Garibaldi, Gap program

Wikipedia, Article on e_8


Given a vector of 8 nonnegative integers, the Weyl dimension formula tells you the dimension of the corresponding irreducible representation. The list of such dimensions is then sorted numerically.


The highest weight 00000000 corresponds to the 1-dimensional module on which E8 acts trivially. The smallest faithful representation of E8 is the adjoint representation of dimension 248 (the second term in the sequence), with highest weight 00000001. The smallest non-fundamental representation has dimension 27000 (the fourth term), corresponding to the highest weight 00000002.


(GAP) # see program given in link.


Cf. A121736, A121737, A121738, A121739, A104599, A121741, A121214, A030650.

Sequence in context: A242763 A200426 A109476 * A028525 A135046 A027654

Adjacent sequences:  A121729 A121730 A121731 * A121733 A121734 A121735




Skip Garibaldi (skip(AT)mathcs.emory.edu), Aug 18 2006



Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

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

Last modified December 22 04:20 EST 2014. Contains 252328 sequences.