207 research outputs found
Multiple partitions, lattice paths and a Burge-Bressoud-type correspondence
A bijection is presented between (1): partitions with conditions
and , where is the frequency of the
part in the partition, and (2): sets of ordered partitions such that
and ,
where is the number of parts in . This bijection entails an
elementary and constructive proof of the Andrews multiple-sum enumerating
partitions with frequency conditions. A very natural relation between the
ordered partitions and restricted paths is also presented, which reveals our
bijection to be a modification of Bressoud's version of the Burge
correspondence.Comment: 12 pages; minor corrections, version to appear in Discrete Mat
Embedding of bases: from the M(2,2k+1) to the M(3,4k+2-delta) models
A new quasi-particle basis of states is presented for all the irreducible
modules of the M(3,p) models. It is formulated in terms of a combination of
Virasoro modes and the modes of the field phi_{2,1}. This leads to a fermionic
expression for particular combinations of irreducible M(3,p) characters, which
turns out to be identical with the previously known formula. Quite remarkably,
this new quasi-particle basis embodies a sort of embedding, at the level of
bases, of the minimal models M(2,2k+1) into the M(3,4k+2-delta) ones, with 0
\leq delta \leq 3.Comment: corrected a typo in the title, 7 page
New path description for the M(k+1,2k+3) models and the dual Z_k graded parafermions
We present a new path description for the states of the non-unitary
M(k+1,2k+3) models. This description differs from the one induced by the
Forrester-Baxter solution, in terms of configuration sums, of their
restricted-solid-on-solid model. The proposed path representation is actually
very similar to the one underlying the unitary minimal models M(k+1,k+2), with
an analogous Fermi-gas interpretation. This interpretation leads to fermionic
expressions for the finitized M(k+1,2k+3) characters, whose infinite-length
limit represent new fermionic characters for the irreducible modules. The
M(k+1,2k+3) models are also shown to be related to the Z_k graded parafermions
via a (q to 1/q) duality transformation.Comment: 43 pages (minor typo corrected and minor rewording in the
introduction
Fermionic characters for graded parafermions
Fermionic-type character formulae are presented for charged
irreduciblemodules of the graded parafermionic conformal field theory
associated to the coset . This is obtained by counting the
weakly ordered `partitions' subject to the graded exclusion principle.
The bosonic form of the characters is also presented.Comment: 24 p. This corrects typos (present even in the published version) in
eqs (4.4), (5.23), (5.24) and (C.4
SM(2,4k) fermionic characters and restricted jagged partitions
A derivation of the basis of states for the superconformal minimal
models is presented. It relies on a general hypothesis concerning the role of
the null field of dimension . The basis is expressed solely in terms of
modes and it takes the form of simple exclusion conditions (being thus a
quasi-particle-type basis). Its elements are in correspondence with
-restricted jagged partitions. The generating functions of the latter
provide novel fermionic forms for the characters of the irreducible
representations in both Ramond and Neveu-Schwarz sectors.Comment: 12 page
Particles in RSOS paths
We introduce a new representation of the paths of the Forrester-Baxter RSOS
models which represents the states of the irreducible modules of the minimal
models M(p',p). This representation is obtained by transforming the RSOS paths,
for the cases p> 2p'-2, to new paths for which horizontal edges are allowed at
certain heights. These new paths are much simpler in that their weight is
nothing but the sum of the position of the peaks. This description paves the
way for the interpretation of the RSOS paths in terms of fermi-type charged
particles out of which the fermionic characters could be obtained
constructively. The derivation of the fermionic character for p'=2 and p=kp'+/-
1 is outlined. Finally, the particles of the RSOS paths are put in relation
with the kinks and the breathers of the restricted sine-Gordon model.Comment: 15 pages, few typos corrected, version publishe
Graded parafermions: standard and quasi-particle bases
Two bases of states are presented for modules of the graded parafermionic
conformal field theory associated to the coset \osp(1,2)_k/\uh(1). The first
one is formulated in terms of the two fundamental (i.e., lowest dimensional)
parafermionic modes. In that basis, one can identify the completely reducible
representations, i.e., those whose modules contain an infinite number of
singular vectors; the explicit form of these vectors is also given.
The second basis is a quasi-particle basis, determined in terms of a modified
version of the \ZZ_{2k} exclusion principle. A novel feature of this model is
that none of its bases are fully ordered and this reflects a hidden structural
exclusion principle.Comment: Harvmac 24 p; minor corrections in eqs 5.2 and 5.
Parafermionic character formulae
We study various aspects of parafermionic theories such as the precise field
content, a description of a basis of states (that is, the counting of
independent states in a freely generated highest-weight module) and the
explicit expression of the parafermionic singular vectors in completely
irreducible modules. This analysis culminates in the presentation of new
character formulae for the parafermionic primary fields. These characters
provide novel field theoretical expressions for \su(2) string functions.Comment: Harvmac (b mode : 37 p
Nonlocal operator basis from the path representation of the M(k+1,k+2) and the M(k+1,2k+3) minimal models
We reinterpret a path describing a state in an irreducible module of the
unitary minimal model M(k+1,k+2) in terms of a string of charged operators
acting on the module's ground-state path. Each such operator acts non-locally
on a path. The path characteristics are then translated into a set of
conditions on sequences of operators that provide an operator basis. As an
application, we re-derive the vacuum finite fermionic character by constructing
the generating function of these basis states.
These results generalize directly to the M(k+1,2k+3) models, the close
relatives of the unitary models in terms of path description.Comment: 22 pages, new title and abstract; section 1 rewritten and section 2.2
improved; version to appear in J. Phys.
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