

A121739


Dimensions of the irreducible representations of the simple Lie algebra of type D4 over the complex numbers, listed in increasing order.


7



1, 8, 28, 35, 56, 112, 160, 224, 294, 300, 350, 567, 672, 840, 1296, 1386, 1400, 1568, 1680, 1925, 2400, 2640, 2800, 3675, 3696, 4096, 4312, 4536, 4719, 5775, 6160, 6600, 7392, 7776, 7840, 8008, 8800, 8910, 8918, 10752, 12320, 12936, 13013, 13728, 15015
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OFFSET

1,2


COMMENTS

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


REFERENCES

N. Bourbaki, Lie groups and Lie algebras, Chapters 46, Springer, 2002.
J. E. Humphreys, Introduction to Lie algebras and representation theory, Springer, 1997.


LINKS

Table of n, a(n) for n=1..45.
Wikipedia, Triality


FORMULA

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.


EXAMPLE

The highest weight 0000 corresponds to the 1dimensional module on which D4 acts trivially. The second second term in the sequence is 8, corresponding to the three inequivalent representations with highest weights 1000, 0010 and 0001 respectively. The third term in the sequence is 28, corresponding to the adjoint representation, which has highest weight 0100.


PROG

(GAP) # see program at sequence A121732


CROSSREFS

Cf. A121732, A121736, A121737, A121738, A104599.
Sequence in context: A006377 A319233 A323198 * A166729 A202290 A131850
Adjacent sequences: A121736 A121737 A121738 * A121740 A121741 A121742


KEYWORD

nonn


AUTHOR

Skip Garibaldi (skip(AT)member.ams.org), Aug 19 2006


STATUS

approved



