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Search: id:A121738
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| A121738 |
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Dimensions of the irreducible representations of the simple Lie algebra of type F4 over the complex numbers, listed in increasing order. |
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7
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| 1, 26, 52, 273, 324, 1053, 1274, 2652, 4096, 8424, 10829, 12376, 16302, 17901, 19278, 19448, 29172, 34749, 76076, 81081, 100776, 106496, 107406, 119119, 160056, 184756, 205751, 212992, 226746, 340119, 342056, 379848, 412776, 420147, 627912
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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We include "1" for the 1-dimensional trivial representation and we list each dimension once, ignoring the possibility that inequivalent representations may have the same dimension.
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REFERENCES
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N. Bourbaki, Lie groups and Lie algebras, Chapter 4-6, Springer, 2002.
J. E. Humphreys, Introduction to Lie algebras and representation theory, Springer, 1997.
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LINKS
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Wikipedia article on F4
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FORMULA
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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.
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EXAMPLE
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The highest weight 0000 corresponds to the 1-dimensional module on which F4 acts trivially. The smallest faithful representation of F4 is the "standard" representation of dimension 26 (the second term in the sequence), with highest weight 0001. (This representation is typically viewed as the trace zero elements in a 27-dimensional exceptional Jordan algebra.) The adjoint representation has dimension 52 (the third term in the sequence) and highest weight 1000.
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PROGRAM
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(GAP) # see program at A121732
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CROSSREFS
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Cf. A121732, A121736, A121737, A121739, A104599, A121741.
Adjacent sequences: A121735 A121736 A121737 this_sequence A121739 A121740 A121741
Sequence in context: A158060 A122999 A040650 this_sequence A043331 A023701 A031459
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KEYWORD
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nonn
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AUTHOR
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Skip Garibaldi (skip(AT)member.ams.org), Aug 19 2006
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