{"paper":{"title":"Translation principle for Dirac index","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"David A. Vogan Jr, Pavle Pand\\v{z}i\\'c, Salah Mehdi","submitted_at":"2015-04-30T17:01:57Z","abstract_excerpt":"Let $G$ be a finite cover of a closed connected transpose-stable subgroup of $GL(n,\\bR)$ with complexified Lie algebra $\\frg$. Let $K$ be a maximal compact subgroup of $G$, and assume that $G$ and $K$ have equal rank. We prove a translation principle for the Dirac index of virtual $(\\frg,K)$-modules. As a byproduct, to each coherent family of such modules, we attach a polynomial on the dual of the compact Cartan subalgebra of $\\frg$. This ``index polynomial'' generates an irreducible representation of the Weyl group contained in the coherent continuation representation. We show that the index "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.08307","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"}