p-adic analog of the kazhdan -Lusztig hypothesis

Classification of unitary representations in irreducible representations of general linear group (non-Archimedean case)

“…[19] where they proved Zeievinsky conjecture on ( : Irr -> Irr from [34]. It is also possible to prove this conjecture for representations < a (n, d)^ ) using Theorem 7.1 as it was done in the previous draft of this paper.…”

“…extends to an involutive automorphism ( : R -> R of the graded ring R. It is announced in [33], [34] and [2] that Irr^Irr.…”

Induced Representations of Affine Hecke Algebras and Canonical Bases of Quantum Groups

“…Zelevinsky has introduced the following partial order on M [Ze1,Ze2]. We say that two segments s and s ′ are linked when t = s ∪ s ′ is a segment and t is different from s and s ′ .…”

“…Theorem 5 ( [Ze2], [CG]) The composition multiplicity of the simple module L n in the induced module M m is equal to…”

Unique functionals and representations of Hecke algebras

“…These had already been classified in the case of GL n by Zelevinsky [1980]. It was known from [Zelevinsky 1981] that there were analogies between this problem and the decomposition of Verma modules of a semisimple Lie algebra into irreducibles, where deep connections with the theory of Hecke algebras had been found by Kazhdan and Lusztig [1979]. Rogawski sought to clarify the relationship between p-adic representation theory and Kazhdan-Lusztig theory.…”