Higher level Fock spaces and affine Yangian

2016/07/12 by Ryosuke Kodera, Kodera, Ryosuke
Mathematics · #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1607.03237

openalex publication_date 2016/07/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct actions of the affine Yangian of type A on higher level Fock spaces by extending known actions of the Yangian of finite type A due to Uglov. This is a degenerate analog of a result by Takemura-Uglov, which constructed actions of the quantum toroidal algebra on higher level q-deformed Fock spaces.

Related

• Affine Yangian action on the Fock space
• Yangian actions on higher level irreducible integrable modules of affine gl(N)
• Level-0 action of U_q(sl_n) on the q-deformed Fock spaces
• Toroidal actions on level 1 modules of U_q(sl_n)
• Notes on Fock space