Geometric construction of the global base of the quantum modified algebra of affine GL_N

1999/03/02 by Olivier Schiffmann, O. Schiffmann, Schiffmann, O. +3 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA) #math.QA

paper · pdf · doi:10.48550/arxiv.math/9903018

12 pages, AMS-TeX

arxiv created 1999/03/02 · openalex publication_date 1999/03/02 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that the global base of the modified quantum algebra of affine GL_N is compatible with the intersection cohomology base of the convolution algebra of the affine flag variety. As a consequence we prove a recent conjecture of Lusztig on the compatibility of the intersection cohomology base with respect to transfer maps.

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• Canonical bases of tensor products and positivity properties

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