Symmetric weights and s-representations

Symmetric weights and s-representations Article

Console, S, Fino, A. (2000). Symmetric weights and s-representations . Kodai Mathematical Journal, 23(2), 266-280. 10.2996/kmj/1138044216

We study irreducible representations of compact Lie groups relating an algebraic condition (the highest weight λ is “symmetric”, i.e., in any simple factor all non zero <λ, α> are equal, for any positive root α and any invariant inner product) with a geometnc one (for all orbits, the d-th osculating space coincides with the representation space). We prove that, if d - 2 and λ is symmetric, the irreducible representation with highest weight λ corresponds to the isotropy representation of a symmetric space. © 2000, Department of Mathematics, Tokyo Institute of Technology. All rights reserved.