The OEIS is supported by the many generous donors to the OEIS Foundation.



Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 60th year, we have over 367,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give
(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. 16
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.
Skip Garibaldi, Gap program
Wikipedia, E8 (mathematics)
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.
Sequence in context: A109478 A200426 A109476 * A028525 A135046 A027654
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 | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 11 14:18 EST 2023. Contains 367727 sequences. (Running on oeis4.)