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 A121214 Dimensions of the irreducible representations of the algebraic group SL4 (equivalently, simple Lie algebra of type A3) over the complex numbers, listed in increasing order. 4
 1, 4, 6, 10, 15, 20, 35, 36, 45, 50, 56, 60, 64, 70, 84, 105, 120, 126, 140, 160, 165, 175, 189, 196, 216, 220, 224, 256, 270, 280, 286, 300, 315, 336, 360, 364, 384, 396, 420, 440, 455, 480, 500, 504, 540, 560, 594, 616, 630, 640, 680, 715, 729, 735, 750, 756 (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. 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, Special linear group FORMULA Given a vector of 3 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 000 corresponds to the 1-dimensional module on which SL4 acts trivially. The standard representation and its dual have dimension 4 (the second term in the sequence) and highest weights 100 and 001. The third term in the sequence, 6, is the dimension of the representation of SL4 on the second exterior power of the standard representation; it has highest weight 010. The fourth term, 10, is the dimension of the second symmetric power of the standard representation or its dual, with highest weight 200 or 002. The fifth term, 15, corresponds to the adjoint representation with highest weight 101. PROG (GAP) # see program at A121732 CROSSREFS Cf. A121732, A121741. Sequence in context: A310585 A179445 A310586 * A219047 A116996 A004399 Adjacent sequences: A121211 A121212 A121213 * A121215 A121216 A121217 KEYWORD nonn AUTHOR Skip Garibaldi (skip(AT)member.ams.org), Aug 20 2006 STATUS approved

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Last modified December 11 13:16 EST 2023. Contains 367727 sequences. (Running on oeis4.)