A geometric Schur-Weyl duality for quotients of affine Hecke algebras
Guillaume Pouchin
TL;DR
This paper develops a geometric Schur-Weyl duality framework for quotients of affine Hecke algebras, extending it to positive parts and linking to cyclotomic Hecke algebras with canonical bases.
Contribution
It introduces a new geometric duality for quotients of affine Hecke algebras, including positive parts and their ideals, connecting to cyclotomic Hecke algebras.
Findings
Established geometric Schur-Weyl duality in type A
Extended duality to positive parts of affine algebras
Identified quotients with cyclotomic Hecke algebras
Abstract
After establishing a geometric Schur-Weyl duality in a general setting, we recall this duality in type A in the finite and affine case. We extend the duality in the affine case to positive parts of the affine algebras. The positive parts have nice ideals coming from geometry, allowing duality for quotients. Some of the quotients of the positive affine Hecke algebra are then identified to some cyclotomic Hecke algebras and the geometric setting allows the construction of canonical bases.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Finite Group Theory Research · Advanced Combinatorial Mathematics