{"paper":{"title":"$P$-alcoves, parabolic subalgebras and cocenters of affine Hecke algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.RT","authors_text":"Sian Nie, Xuhua He","submitted_at":"2013-10-15T07:38:49Z","abstract_excerpt":"This is a continuation of the sequence of papers \\cite{HN2}, \\cite{H99} in the study of the cocenters and class polynomials of affine Hecke algebras $\\ch$ and their relation to affine Deligne-Lusztig varieties. Let $w$ be a $P$-alcove element, as introduced in \\cite{GHKR} and \\cite{GHN}. In this paper, we study the image of $T_w$ in the cocenter of $\\ch$. In the process, we obtain a Bernstein presentation of the cocenter of $\\ch$. We also obtain a comparison theorem among the class polynomials of $\\ch$ and of its parabolic subalgebras, which is analogous to the Hodge-Newton decomposition theor"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.3940","kind":"arxiv","version":1},"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"}