Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Perfect Crystals and q-deformed Fock Spaces   A general scheme for the wedge construction of q-deformed Fock spaces using
the theory of perfect crystals is presented.
  Let $U_q(\g)$ be a quantum affine algebra. Let $V$ be a finite-dimensional
$U'_q(\g)$-module with a perfect crystal base of level~$l$. Let $V_\aff\simeq
V\otimes\C[z,z^{-1}]$ be the affinization of $V$, with crystal base
$(L_\aff,B_\aff)$. The wedge space $V_\aff\wedge V_\aff$ is defined as the
quotient of $V_\aff\otimes V_\aff$ by the subspace generated by the action of
$U_q(\g)[z^a\otimes z^b +z^b\otimes z^a]_{a,b\in\Z}$ on $v\otimes v$ ($v$ an
extremal vector). The wedge space $\bigwedge^r V_\aff$ ($r\in\N$) is defined
similarly. Normally ordered wedges are defined by using the energy function
$H:B_\aff\otimes B_\aff\to\Z$. Under certain assumptions, it is proved that
normally ordered wedges form a base of $\bigwedge^r V_\aff$.
  A q-deformed Fock space is defined as the inductive limit of $\bigwedge^r
V_\aff$ as $r\to\infty$, taken along the semi-infinite wedge associated to a
ground state sequence. It is proved that normally ordered wedges form a base of
the Fock space and that the Fock space has the structure of an integrable
$U_q(\g)$-module. An action of the bosons, which commute with the
$U'_q(\g)$-action, is given on the Fock space. It induces the decomposition of
the q-deformed Fock space into the tensor product of an irreducible
$U_q(\g)$-module and a bosonic Fock space.
  As examples, Fock spaces for types $A^{(2)}_{2n}$, $B^{(1)}_n$,
$A^{(2)}_{2n-1}$, $D^{(1)}_n$ and $D^{(2)}_{n+1}$ at level~1 and $A^{(1)}_1$ at
level~$k$ are constructed. The commutation relations of the bosons in each of
these cases are calculated, using two point functions of vertex operators.

1
The categories of this paper are: cs
19
The categories of this paper are: eess
9
The categories of this paper are: nlin
5
The categories of this paper are: gr-qc
18
The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
24
The categories of this paper are: dg-ga
26
The categories of this paper are: bayes-an
3
The categories of this paper are: physics
10
The categories of this paper are: q-bio
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
8
The categories of this paper are: hep-ex