TORUS FIXED POINT SETS OF HESSENBERG SCHUBERT VARIETIES IN REGULAR SEMISIMPLE HESSENBERG VARIETIES

It is well-known that the T-fixed points of a Schubert variety in the flag variety GLn(C)/B can be characterized purely combinatorially in terms of Bruhat order on the symmetric group Sn. In a recent preprint, Cho, Hong, and Lee give a combinatorial description of the T-fixed points of Hessenberg analogues of Schubert varieties (which we call Hessenberg Schubert varieties) in a regular semisimple Hessenberg variety. This note gives an interpretation of their result in terms of Bruhat order by making use of a partition of the symmetric group defined using so-called subsets of Weyl type. The Appendix, written by Michael Zeng, proves a lemma concerning subsets of Weyl type which is required in our arguments.