{"paper":{"title":"Computing the associatied cycles of certain Harish-Chandra modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"David Vogan, Pavle Pandzic, Roger Zierau, Salah Mehdi","submitted_at":"2017-12-12T08:36:14Z","abstract_excerpt":"Let $G_{\\mathbb{R}}$ be a simple real linear Lie group with maximal compact subgroup $K_{\\mathbb{R}}$ and assume that ${\\rm rank}(G_\\mathbb{R})={\\rm rank}(K_\\mathbb{R})$. In \\cite{MPVZ} we proved that for any representation $X$ of Gelfand-Kirillov dimension $\\frac{1}{2}\\dim(G_{\\mathbb{R}}/K_{\\mathbb{R}})$, the polynomial on the dual of a compact Cartan subalgebra given by the dimension of the Dirac index of members of the coherent family containing $X$ is a linear combination, with integer coefficients, of the multiplicities of the irreducible components occurring in the associated cycle. In t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.04173","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"}