Gröbner fans of Specht ideals

Abstract

In this paper, we give the Gröbner fan and the state polytope of a Specht ideal $I_{\lambda }$ explicitly. In particular, we show that the state polytope of $I_{\lambda }$ for a partition $\lambda =({\lambda }_1,\dots ,{\lambda }_m)$ is always a generalized permutohedron, and it is a (usual) permutohedron if and only if ${\lambda }_{i-1}={\lambda }_i>0$ for some $i$.

Exposition expanded, for example, Lemma 2.9 added. 11 pages, comments welcome