math.RT — Representation Theory
We prove Lusztig's sharp boundedness conjecture for Hecke algebras of finite-rank Coxeter systems with positive integer-valued weight functions.
math.RT — Representation Theory
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.