Fermionic $q$-Fock Space and Braided Geometry

Abstract

We write the fermionic $q$-Fock space representation of $U_q(\widehat{s{l}_n})$ as an infinite extended braided tensor product of finite-dimensional fermionic $U_q(s{l}_n)$-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 $[b_2,b_{-2}]=2(\frac{1-q^{-4n}}{1-q^{-4}})$. Our R-matrix approach includes other Hecke R-matrices as well.

LATEX 12 pages

References in corpus (1)

• Introduction to Braided Geometry and $q$-Minkowski Space