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 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS We include "1" for the 1-dimensional 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 (r-s)*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 = r-s, y = r+s, and z = -x-y. - Elliott Line, Dec 22 2020 REFERENCES N. Bourbaki, Lie groups and Lie algebras, Chapters 4-6, 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

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Last modified May 11 10:31 EDT 2021. Contains 343788 sequences. (Running on oeis4.)