Quantum Toroidal Algebras and Their Vertex Representations

Yoshihisa Saito

doi:10.2977/prims/1195144759

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Quantum Toroidal Algebras and Their Vertex Representations

Yoshihisa Saito

Year: 1998 Journal: Publications of the Research Institute for Mathematical Sciences Vol: 34 (2)Pages: 155-177 Publisher: Kyoto University

DOI: 10.2977/prims/1195144759

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Abstract

We construct the vertex representations of the quantum toroidal algebras U_q(\mathfrak{sl}_{n+ 1,\mathit{tor}}) . In the classical case the vertex representations are not irreducible. However in the quantum case they are irreducible.

Keywords:

Mathematics Vertex (graph theory) Quantum Toroid Pure mathematics Combinatorics Quantum mechanics Physics Graph

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Algebraic structures and combinatorial models

Physical Sciences → Mathematics → Geometry and Topology

Advanced Topics in Algebra

Physical Sciences → Mathematics → Algebra and Number Theory

Quantum many-body systems

Physical Sciences → Physics and Astronomy → Atomic and Molecular Physics, and Optics

Quantum Toroidal Algebras and Their Vertex Representations

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