Fermionic $q$-Fock Space and Braided Geometry

Details Fermionic $q$-Fock Space and Braided Geometry Fermionic $q$-Fock Space and Braided Geometry

1995-12-05

arxiv.org/abs/q-alg/9512006v1

Mathematics

Quantum Algebra

LATEX 12 pages

Scientific paper

We write the fermionic $q$-Fock space representation of $U_q(\hat{sl_n})$ 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 $[b_{2},b_{-2}]=2({1-q^{-4n}\over 1-q^{-4}})$. Our R-matrix approach includes other Hecke R-matrices as well.

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