

A121741


Dimensions of the irreducible representations of the simple Lie algebra of type A2 (equivalently, the group SL3) over the complex numbers, listed in increasing order.


9



1, 3, 6, 8, 10, 15, 21, 24, 27, 28, 35, 36, 42, 45, 48, 55, 60, 63, 64, 66, 78, 80, 81, 90, 91, 99, 105, 120, 125, 132, 136, 143, 153, 154, 162, 165, 168, 171, 190, 192, 195, 210, 216, 224, 231, 234, 253, 255, 260, 270, 273, 276, 280, 288, 300
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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.
Numbers of the form (x * (x  y) * (x  z) + y * (y  x) * (y  z) + z * (z  x) * (z  y)) / 18 with x + y + z = 0 and x * y * z > 0.  Michael Somos, Jun 26 2013
Positive numbers of the form (rs)*r*(r+s) where r and s are integers, i.e., the product of three integers in arithmetic progression. In the expression above, set x = rs, y = r+s, and z = xy.  Elliott Line, Dec 22 2020


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

Andy Huchala, Table of n, a(n) for n = 1..20000
Andy Huchala, Java Program
Wikipedia, The special linear group


PROG

(GAP) # see program at sequence A121732


CROSSREFS

Equals A088915/2.
Cf. A121732, A121736, A121737, A121738, A121739, A104599, A121214.
Sequence in context: A184855 A187336 A169582 * A043549 A228707 A290218
Adjacent sequences: A121738 A121739 A121740 * A121742 A121743 A121744


KEYWORD

nonn


AUTHOR

Skip Garibaldi (skip(AT)member.ams.org), Aug 19 2006, Aug 23 2006


STATUS

approved



