On the action of the symmetric group on the free LAnKe: a question of Friedmann, Hanlon, Stanley and Wachs
Citation:
Maliakas M, Stergiopoulou D-D. On the action of the symmetric group on the free LAnKe: a question of Friedmann, Hanlon, Stanley and Wachs. arXiv [Internet]. Submitted;(2410.06979).
A LAnKe (also known as a Lie algebra of the th kind, or a Filippov algebra) is a vector space equipped with a skew-symmetric -linear form that satisfies the generalized Jacobi identity. The symmetric group acts on the multilinear part of the free LAnKe on generators, where is the number of brackets, by permutation of the generators. The corresponding representation was studied by Friedmann, Hanlon, Stanley and Wachs, who asked whether for , its irreducible decomposition contains no summand whose Young diagram has at most columns. The answer is affirmative if $k \le 3$. In this paper, we show that the answer is affirmative for all $k$
