{"paper":{"title":"Ad-nilpotent ideals and The Shi arrangement","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.CO","authors_text":"Chao-Ping Dong","submitted_at":"2012-05-30T11:13:49Z","abstract_excerpt":"We extend the Shi bijection from the Borel subalgebra case to parabolic subalgebras. In the process, the $I$-deleted Shi arrangement $\\texttt{Shi}(I)$ naturally emerges. This arrangement interpolates between the Coxeter arrangement $\\texttt{Cox}$ and the Shi arrangement $\\texttt{Shi}$, and breaks the symmetry of $\\texttt{Shi}$ in a certain symmetrical way. Among other things, we determine the characteristic polynomial $\\chi(\\texttt{Shi}(I), t)$ of $\\texttt{Shi}(I)$ explicitly for $A_{n-1}$ and $C_n$. More generally, let $\\texttt{Shi}(G)$ be an arbitrary arrangement between $\\texttt{Cox}$ and $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.6632","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}