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Structural Reductions for Lusztig’s Conjectures in Types (B_n), (\widetilde B_n), and (\widetilde C_n)

A mix of human-written and AI-generated textHuman understanding: some partsmath.RT — Representation Theorymath.GR — Group Theory

Contributed by Qiyue Tang ↗

Version 1 / Nov 10, 2026 / CC BY 4.0

Abstract

We develop structural reductions for Lusztig’s conjectures P1–P15 for unequal-parameter Hecke algebras of finite type (B_n) and nonextended affine types (\widetilde B_n) and (\widetilde C_n). The results include integral parabolic propagation mechanisms, reductions of P15 to constant leading-coefficient identities, spectral degree bounds, and finite-facet attainment criteria connecting affine tempered representations with the original Kazhdan–Lusztig filtration. Exact computations verify the relevant identities in the recorded finite-rank cases. These results produce internally audited proof candidates and isolate the remaining comparison and attainment problems required for unconditional all-rank statements.

Provenance statement

The research reported in this paper was developed during an eight-hour research run using GPT-6-Pro. Codex was subsequently used to audit the mathematical arguments and to revise and polish the manuscript. A separate review using Rethlas-OSV is planned and will be reported in a later version.

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Version history

  1. v1 · 78 pagesSubmitted by Qiyue TangInitial depositCurrentNov 08, 2026