{"paper":{"title":"Classification of $A_{\\mathfrak{q}}(\\lambda)$ modules by their Dirac cohomology for type $D$, $G_2$ and $\\mathfrak{sp}(2n,\\mathbb{R})$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Ana Prli\\'c","submitted_at":"2018-02-06T14:47:11Z","abstract_excerpt":"Let $G$ be a connected real reductive group with maximal compact subgroup $K$ of the same rank as $G$. In the recent paper of Huang, Pand\\v{z}i\\'{c} and Vogan, it was shown that the admissible $\\Theta$--stable parabolic subalgebras $\\mathfrak{q}$ of $\\mathfrak{g}$ are in one-to-one correspodence with the faces of $W \\rho$ intersecting the $\\mathfrak{k}$--dominant Weyl chamber and that $A_{\\mathfrak{q}}(0)$--modules can be classified by their Dirac cohomology in geometric terms. They described in detail the cases when $\\mathfrak{g}_0$ is of type $A$, $B$, $F$ and $C$ except for $\\mathfrak{g}_0 "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.01974","kind":"arxiv","version":2},"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"}