DefinitionDefinition: Literature-sourcedProof: Not applicablejudge pass (gpt-5.6-terra)audited 2026-09-05

How statement and proof provenance work

The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.

Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.

These labels describe origin, not correctness: citations and verification chips remain separate evidence.

The Weyl vector rho for a chosen positive system

Definition

Fix a positive root system $Φ^{+}$ as in Triangular decomposition from a chosen positive root system. The Weyl vector for that choice is

$ρ : = \frac{1}{2} \sum_{α \in Φ^{+}} α \in h^{*} .$

This is the shift used in the dot action and in the quadratic Casimir eigenvalue formula on this page.

Depends on

Triangular decomposition from a chosen positive root system

Used by

Dependency tree · two levels

4 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.

Sources

Yiannis Sakellaridis, Verma Modules and the Category O (standard reference, not scraped)