This site is supported by donations to The OEIS Foundation.



Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 4500 articles have referenced us, often saying "we would not have discovered this result without the OEIS".

(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A121738 Dimensions of the irreducible representations of the simple Lie algebra of type F4 over the complex numbers, listed in increasing order. 7
1, 26, 52, 273, 324, 1053, 1274, 2652, 4096, 8424, 10829, 12376, 16302, 17901, 19278, 19448, 29172, 34749, 76076, 81081, 100776, 106496, 107406, 119119, 160056, 184756, 205751, 212992, 226746, 340119, 342056, 379848, 412776, 420147, 627912 (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.


N. Bourbaki, Lie groups and Lie algebras, Chapter 4-6, Springer, 2002.

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


Table of n, a(n) for n=1..35.

Wikipedia article on F<sub>4</sub>


Given a vector of 4 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 0000 corresponds to the 1-dimensional module on which F4 acts trivially. The smallest faithful representation of F4 is the "standard" representation of dimension 26 (the second term in the sequence), with highest weight 0001. (This representation is typically viewed as the trace zero elements in a 27-dimensional exceptional Jordan algebra.) The adjoint representation has dimension 52 (the third term in the sequence) and highest weight 1000.


(GAP) # see program at A121732


Cf. A121732, A121736, A121737, A121739, A104599, A121741.

Sequence in context: A040650 A252994 A214476 * A043331 A023701 A031459

Adjacent sequences:  A121735 A121736 A121737 * A121739 A121740 A121741




Skip Garibaldi (skip(AT)member.ams.org), Aug 19 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 November 25 18:43 EST 2015. Contains 264418 sequences.