Canonical bases of loop algebras via quot schemes II

2004/08/29 by Olivier Schiffmann, Schiffmann, Olivier · 2 citations
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #math.AG #math.QA

paper · pdf · doi:10.48550/arxiv.math/0408401

65 pages Latex

arxiv created 2004/08/29 · openalex publication_date 2004/08/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper is a sequel (and contains a better treatment) of math.QA/0404032; We construct some canonical bases for quantum toroidal algebras of types D₄, E₆, E₇, E₈ using perverse sheaves on quot schemes parametrizing equivariant coherent sheaves on elliptic curves. We also study some compatibility properties of these bases with some natural filtrations and modules.

Cited by

• Lectures on canonical and crystal bases of Hall algebras
• Higgs bundles on weighted projective lines and loop crystals

Related

• Canonical bases of loop algebras via Quot schemes, I
• Noncommutative projective curves and quantum loop algebras
• Perverse sheaves and quantum Grothendieck rings
• Combinatorial bases in quantum toroidal \mathfrakgl₂ modules
• The PBW basis of U_q,q(\mathfrakgl_n)