Fermionic characters for graded parafermions

Bégin, Luc; Fortin, Jean-François; Jacob, P.; Mathieu, Pierre

doi:10.1016/s0550-3213(03)00175-5

Cited by 13 publications

(44 citation statements)

References 11 publications

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“…In the following, we trade the pair (i, σi) for (x, y). 3 References [39,38] are early studies of the relation between these generalized RSOS models and the non-unitary minimal models. 4 There is also a simple path description for the M(2, 2k + 1) models but it is not formulated directly in terms of RSOS paths of [21]; it is expressed in terms of a different type of paths, the so-called Bressoud paths [8], to be introduced below.…”

Section: Introductionmentioning

confidence: 99%

A new path description for the {\cal M} (k+1,2k+3) models and the dual {\cal Z}_k graded parafermions

Jacob

Mathieu

2007

J. Stat. Mech.

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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 ↔ q −1 ) duality transformation.

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Section: Introductionmentioning

confidence: 99%

A new path description for the {\cal M} (k+1,2k+3) models and the dual {\cal Z}_k graded parafermions

Jacob

Mathieu

2007

J. Stat. Mech.

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“…5 The relative sign in (11) indicates that ψ 1 and ψ † 1 are mutually fermionic. The one in (13) shows that ψ 1 is not fermionic with respect to itself.…”

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confidence: 99%

The Zk(su(2),3/2) parafermions

Jacob

Mathieu

2005

Physics Letters B

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We introduce a novel parafermionic theory for which the conformal dimension of the basic parafermion is 3 2 (1 − 1/k), with k even. The structure constants and the central charges are obtained from modetype associativity calculations. The spectrum of the completely reducible representations is also determined. The primary fields turns out to be labeled by two positive integers instead of a single one for the usual parafermionic models. The simplest singular vectors are also displayed. It is argued that these models are equivalent to the non-unitary minimal W k (k + 1, k + 3) models. More generally, we expect all W k (k + 1, k + 2β) models to be identified with generalized parafermionic models whose lowest dimensional parafermion has dimension β(1 − 1/k). *

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“…Given an overpartition, we put all the overlined parts in one partition and the rest in the other partition. For example, starting with the overpartition (8, 6, 6, 4, 4,4, 2,1), we get (4, 1) and (8,6,6,4,4,2).…”

Section: Combinatorial Setting and Applicationsmentioning

confidence: 99%

“…. ) [4], [6], [14], [18], [22], [23], [24], [27]. First asymptotic and probabilistic results on overpartitions were presented in [11].…”

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confidence: 99%

A Local Limit Theorem in the Theory of Overpartitions

2006

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An overpartition of an integer n is a partition where the last occurrence of a part can be overlined. We study the weight of the overlined parts of an overpartition counted with or without their multiplicities. This is a continuation of a work by Corteel and Hitczenko where it was shown that the expected weight of the overlined parts is asymptotic to n/3 as n → ∞ and that the expected weight of the overlined parts counted with multiplicity is n/2. Here we refine these results. We first compute the asymptotics of the variance of the weight of the overlined parts counted with multiplicity. We then asymptotically evaluate the probability that the weight of the overlined parts is n/3 ± k for k = o(n) and the probability that the weight of the overlined parts counted with multiplicity is n/2 ± k for k = o(n). The first computation is straightforward and uses known asymptotics of partitions. The second one is more involved and requires a sieve argument and the application of the saddle-point method. From that we can directly evaluate the probability that two random partitions of n do not share a part.

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Fermionic characters for graded parafermions

Cited by 13 publications

References 11 publications

A new path description for the {\cal M} (k+1,2k+3) models and the dual {\cal Z}_k graded parafermions

A new path description for the {\cal M} (k+1,2k+3) models and the dual {\cal Z}_k graded parafermions

The Zk(su(2),3/2) parafermions

A Local Limit Theorem in the Theory of Overpartitions

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