Geometric Construction of Highest Weight Crystals for Quantum Generalized Kac-Moody Algebras
Seok-Jin Kang, Masaki Kashiwara, Olivier Schiffmann
TL;DR
This paper introduces a geometric method to construct highest weight crystals for quantum generalized Kac-Moody algebras using irreducible components of Lagrangian subvarieties in Nakajima's quiver varieties.
Contribution
It provides a novel geometric construction of highest weight crystals for quantum generalized Kac-Moody algebras via Lagrangian subvarieties of quiver varieties.
Findings
Constructs highest weight crystals geometrically.
Uses irreducible components of Lagrangian subvarieties.
Connects quiver varieties with quantum algebra representations.
Abstract
We present a geometric construction of highest weight crystals for quantum generalized Kac-Moody algebras. It is given in terms of the irreducible components of certain Lagrangian subvarieties of Nakajima's quiver varieties associated to quivers with edge loops.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Combinatorial Mathematics · Nonlinear Waves and Solitons