Commentarii Mathematici Helvetici


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Volume 76, Issue 3, 2001, pp. 515–575
DOI: 10.1007/PL00013217

On simply laced Lie algebras and their minuscule representations

J. Lurie[1]

(1) The Graduate College, Princeton University, 88 College Road West, NJ 08544, PRINCETON, UNITED STATES

In this paper we adapt a known construction for the simply laced, semisimple Lie algebras (over Z), and thereby obtain a very simple construction for all minuscule representations of those Lie algebras (again over Z). We apply these results to give explicit formulas for tensors invariant under the exceptional algebras $ E_6 $ and $ E_7 $.

Keywords: Exceptional algebras, minuscule representations

Lurie J. On simply laced Lie algebras and their minuscule representations. Comment. Math. Helv. 76 (2001), 515-575. doi: 10.1007/PL00013217