Automorphism group of the crown-weight space (Q2581462)

The authors present a study of the crown-weight space (i.e. the space \((\mathbb F^{2m}_q,w_{\text{CR}})\), for the crown \(\text{CR}=\text{CR}_{2m}\) and determine the structure of the automorphism group \(\text{Aut}(\mathbb F^{2m}_q,w_{\text{CR}})\). In a way, the group of all weight-preserving linear automorphisms of finite-dimensional vector spaces over a finite field equipped with crown weight has been determined. In general, it seems to be an interesting problem to determine the structure of \(\text{Aut}(\mathbb F^n_q,w_p)\) for a given poset \(P\).