login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

%I

%S 1,3,6,8,10,15,21,24,27,28,35,36,42,45,48,55,60,63,64,66,78,80,81,90,

%T 91,99,105,120,125,132,136,143,153,154,162,165,168,171,190,192,195,

%U 210,216,224,231,234,253,255,260,270,273,276,280,288,300

%N 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.

%C 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.

%C 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

%C 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

%D N. Bourbaki, Lie groups and Lie algebras, Chapters 4-6, Springer, 2002.

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

%H Andy Huchala, <a href="/A121741/b121741.txt">Table of n, a(n) for n = 1..20000</a>

%H Andy Huchala, <a href="/A121741/a121741.java.txt">Java Program</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Special_linear_group">The special linear group</a>

%o (GAP) # see program at sequence A121732

%Y Equals A088915/2.

%Y Cf. A121732, A121736, A121737, A121738, A121739, A104599, A121214.

%K nonn

%O 1,2

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 13 11:30 EDT 2021. Contains 344990 sequences. (Running on oeis4.)