Fermionic q-Fock Space and Braided Geometry

1995/12/05 by Shahn Majid, S. Majid, Majid, S.
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #math.QA #q-alg

paper · pdf · doi:10.48550/arxiv.q-alg/9512006

LATEX 12 pages

arxiv created 1995/12/05 · openalex publication_date 1995/12/05 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We write the fermionic q-Fock space representation of U_q(sl_n) as an infinite extended braided tensor product of finite-dimensional fermionic U_q(sl_n)-quantum planes or exterior algebras. Using braided geometrical techniques developed for such quantum exterior algebras, we provide a new approach to the Kashiwara-Miwa-Stern action of the Heisenberg algebra on the q-fermionic Fock space, obtaining the action in detail for the lowest nontrivial case [b₂,b_-2]=2(1-q^-4n\over 1-q^-4). Our R-matrix approach includes other Hecke R-matrices as well.

Citations

• Introduction to Braided Geometry and q-Minkowski Space

Related

• Bosonic and Fermionic Representations of Endomorphisms of Exterior Algebras
• Decomposition of q-deformed Fock spaces
• Double-loop algebras and the Fock space
• Braided products for quantum spaces
• Notes on Fock space