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

By Bernard Leclerc, M. Nazarov, Jean-Yves Thibon. 2000

58 citations recorded by the source corpus.

A criterion of irreducibility for induction products of evaluation modules of type A affine Hecke algebras is given. It is derived from multiplicative properties of the canonical basis of a quantum deformation of the Bernstein—Zelevinsky ring.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/a088d3008806df5fa611ce89277b10ae381ca485

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In Algebra and Number Theory

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Citations in the corpus

Representations of Khovanov–Lauda–Rouquier algebras and combinatorics of Lyndon words (2009, background): “5 and [14] it is reasonable to consider the following”
Dual canonical bases and Kazhdan–Lusztig polynomials☆ (2005, methodology): “it is the basis dual to the canonical basis of U+ m+n under a natural bilinear form normalized as in [ LNT , §3.4].”
On parabolic induction on inner forms of the general linear group over a non-archimedean local field (2014, result): “18 is consistent with the results of [36] in the case where both Z(m) and Z(m) are ladders satisfying b(∆i+1) = b( ← ∆i) for all i = 1, .”
A Quantum Cluster Algebra of Kronecker Type and the Dual Canonical Basis (2010, background): “The corresponding version for dual canonical bases is described in [28], [32], and [25]; in our example the characterization is Theorem 4.1.”
Representations of Shifted Yangians and Finite W-algebras (2005, methodology): “The final result gives a criterion for the irreducibility of the standard module V (A), in the spirit of [ LNT ].”