Semiinfinite $q$wedge construction of the level 2 Fock Space of $U_q(\affsl{2})$
Abstract
In this proceedings a particular example from \cite{KMPY} (qalg/9603025) is presented: the construction of the level 2 Fock space of $\U_q(\affsl{2})$. The generating ideal of the wedge relations is given and the wedge space defined. Normal ordering of wedges is defined in terms of the energy function. Normally ordered wedges form a base of the wedge space. The qdeformed Fock space is defined as the space of semiinfinite wedges with a finite number of vectors in the wedge product differing from a ground state sequence, and endowed with a separated qadic topology . Normally ordered wedges form a base of the Fock space. The action of $\U_q(\affsl{2})$ on the Fock space converges in the qadic topology. On the Fock space the action of bosons, which commute with the $\U_q(\affsl{2})$action, also converges in the qadic topology. Hence follows the decomposition of the Fock space into irreducible $\U_q(\affsl{2})$modules.
 Publication:

eprint arXiv:qalg/9701040
 Pub Date:
 January 1997
 DOI:
 10.48550/arXiv.qalg/9701040
 arXiv:
 arXiv:qalg/9701040
 Bibcode:
 1997q.alg.....1040H
 Keywords:

 Mathematics  Quantum Algebra;
 17B37 (Primary) 81R10 (Secondary)
 EPrint:
 11 pages, LaTeX (requires amslatex1.2 and amsfonts). Invited talk at the NankaiCRM meeting ``Extended and quantum algebras and their application to physics'', held at the Nankai Institute for Mathematics, Nankai University, Tianjin, China, 1924 August 1996