738 research outputs found
Surface operator content of the A_L face models
A set of fixed boundary weights for both the critical dense and dilute A_L
face models is constructed from the known boundary weights of the related loop
model. The surface operator content and the conformal partition functions then
follow from the results obtained via the Bethe equations.Comment: 12 pages, LaTeX, 2 eps figs, Elsevier style files, to appear in the
Hans van Leeuwen festschrift (Physica A
The Andrews-Gordon identities and -multinomial coefficients
We prove polynomial boson-fermion identities for the generating function of
the number of partitions of of the form , with
, and . The bosonic side of
the identities involves -deformations of the coefficients of in the
expansion of . A combinatorial interpretation for these
-multinomial coefficients is given using Durfee dissection partitions. The
fermionic side of the polynomial identities arises as the partition function of
a one-dimensional lattice-gas of fermionic particles. In the limit
, our identities reproduce the analytic form of Gordon's
generalization of the Rogers--Ramanujan identities, as found by Andrews. Using
the duality, identities are obtained for branching functions
corresponding to cosets of type of fractional level .Comment: 31 pages, Latex, 9 Postscript figure
Extensions of the well-poised and elliptic well-poised Bailey lemma
We establish a number of extensions of the well-poised Bailey lemma and
elliptic well-poised Bailey lemma. As application we prove some new
transformation formulae for basic and elliptic hypergeometric series, and embed
some recent identities of Andrews, Berkovich and Spiridonov in a well-poised
Bailey tree.Comment: 16 pages, AMS-LaTeX, to appear in Indag. Math. (N.S.
The generalized Borwein conjecture. II. Refined q-trinomial coefficients
Transformation formulas for four-parameter refinements of the q-trinomial
coefficients are proven. The iterative nature of these transformations allows
for the easy derivation of several infinite series of q-trinomial identities,
and can be applied to prove many instances of Bressoud's generalized Borwein
conjecture.Comment: 36 pages, AMS-LaTe
Solvable RSOS models based on the dilute BWM algebra
In this paper we present representations of the recently introduced dilute
Birman-Wenzl-Murakami algebra. These representations, labelled by the level-
B, C and D affine Lie algebras, are Baxterized to
yield solutions to the Yang-Baxter equation.
The thus obtained critical solvable models are RSOS counterparts of the,
respectively, D, and B -matrices of
Bazhanov and Jimbo. For the D and B algebras the RSOS
models are new. An elliptic extension which solves the Yang-Baxter equation is
given for all three series of dilute RSOS models.Comment: 25 pages, uuencoded compressed PostScript file, Amsterdam preprint
ITFA-94-2
Critical behaviour of the dilute O(n), Izergin-Korepin and dilute face models: Bulk properties
The analytic, nonlinear integral equation approach is used to calculate the
finite-size corrections to the transfer matrix eigen-spectra of the critical
dilute O(n) model on the square periodic lattice. The resulting bulk conformal
weights extend previous exact results obtained in the honeycomb limit and
include the negative spectral parameter regimes. The results give the operator
content of the 19-vertex Izergin-Korepin model along with the conformal weights
of the dilute face models in all four regimes.Comment: 23 pages, no ps figures, latex file, to appear in NP
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