A339250 List of dimensions for which there exist several non-isomorphic irreducible representations of E6.
27, 351, 1728, 3003, 5824, 7371, 7722, 17550, 19305, 34398, 46332, 51975, 54054, 61425, 78975, 100386, 112320, 146432, 252252, 314496, 359424, 371800, 386100, 393822, 412776, 442442, 459459
Offset: 1
Keywords
Examples
With the fundamental weights numbered as in Bourbaki, the irreducible E6-modules with highest weights [1,0,0,0,0,0] and [0,0,0,0,0,1] both have dimension 77. The vectors [0,0,0,0,1,0], [0,0,1,0,0,0], [2,0,0,0,0,0], and [0,0,0,0,0,2] are the four highest weights which correspond to irreducible representations of dimension 351.
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, E6 (mathematics)
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