Triality, Exceptional Lie Algebras and Deligne Dimension Formulas☆
By J. M. Landsberg, Laurent Manivel. 2001
104 citations recorded by the source corpus.
Abstract We give a computer-free proof of the Deligne, Cohen and de Man formulas for the dimensions of the irreducible g -modules appearing in g ⊗k, k⩽4, where g ranges over the exceptional complex simple Lie algebras. We give additional dimension formulas for the exceptional series, as well as uniform dimension formulas for other representations distinguished by Freudenthal along the rows of his magic chart. Our proofs use the triality model of the magic square, which we review and present a simplified proof of its validity. We conclude with some general remarks about obtaining “series” of Lie algebras in the spirit of Deligne and Vogel.
Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/d9acf901aa404e374ef2b427d0842b6cd01cb40f
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In Algebra and Number Theory
In Discrete Mathematics and Combinatorics
In Geometry and Topology
- Alberto Elduque
- Laurent Manivel
- J. M. Landsberg
- Kazuya Kawasetsu
- Daniele Faenzi
- Tamara G. Kolda
- Brett W. Bader
- E. E. Tyrtyshnikov
Citations in the corpus
- The Intermediate Vertex Subalgebras of the Lattice Vertex Operator Algebras (2013, background): “s of some tensor products of the adjoint representations of the simple Lie algebras in the above exceptional series, remarkable dimension formulas, called Deligne dimension formulas, were established [8, 11, 23]. They are expressed as rational functions in the dual Coxeter number h∨. For example, di”
- The Magic Square and Symmetric Compositions (2004, methodology): “A similar construction has been given by Landsberg and Manivel [ LM1 ,2], inspired by previous work of Allison and Faulkner [AF].”
- A universal dimension formula for complex simple Lie algebras (2004, methodology): “Here F3Gdenotes the two-parameter series of Lie algebras in the generalized third row of Freudenthal’s magic chart, gr(H,A) with a= 1,2,4,8 and r ≥3, which contains sp 2r,sl r,so4 , and e7 when r = 3 [13]. Note that through each classical simple Lie algebra there are an infinite number of lines with ”
- Representation Theory and Projective Geometry (2002, unknown): “A G ] 2 J ul 2 00 2”