# The Andrews–Gordon Identities and q-Multinomial Coefficients

@article{Warnaar1997TheAI,
title={The Andrews–Gordon Identities and q-Multinomial Coefficients
},
author={S. Ole Warnaar},
journal={Communications in Mathematical Physics},
year={1997},
volume={184},
pages={203-232}
}
• S. Warnaar
• Published 15 January 1996
• Mathematics
• Communications in Mathematical Physics
Abstract: We prove polynomial boson-fermion identities for the generating function of the number of partitions of n of the form $n=\sum_{j=1}^{L-1} j f_j$, with $f_1\leq i-1$, $f_{L-1} \leq i'-1$ and $f_j+f_{j+1}\leq k$. The bosonic side of the identities involves q-deformations of the coefficients of xa in the expansion of $(1+x+\cdots+ x^k)^L$. A combinatorial interpretation for these q-multinomial coefficients is given using Durfee dissection partitions. The fermionic side of the…
56 Citations
Semi-Infinite Realization of Unitary Representations of the N=2 Algebra and Related Constructions
• Mathematics
• 2001
AbstractIn the examples of the N=2 super-Virasoro algebra and the affine $$\widehat{s\ell }\left( 2 \right)$$ algebra, we investigate the construction of unitary representations of
The Rogers-Ramanujan identities, the finite general linear groups, and the Hall-Littlewood polynomials
We connect Gordon's generalization of the Rogers-Ramanujan identities with the Hall-Littlewood polynomials and with generating functions which arise in a probabilistic setting in the finite general
Supernomial Coefficients, Polynomial Identities and q-Series
• Mathematics
• 1997
Abstractq-Analogues of the coefficients of xa in the expansion ofΠj=1N(1 + x + ⋯ + xj)Lj are proposed. Useful properties, such as recursion relations, symmetries and limiting theorems of the
Integrable $\hat{\mathfrak{sl}_2}$-modules as infinite tensor products
• Mathematics
• 2002
Using the fusion product of the representations of the Lie algebra $\mathfrak{sl}_2$ we construct a set of the integrable highest weight $\hat{\mathfrak{sl}_2}$-modules $L^D$, depending on the vector
70 10 07 v 1 8 J an 1 99 7 Supernomial coefficients , polynomial identities and q-series
• Mathematics
• 2008
q-Analogues of the coefficients of x in the expansion of ∏N j=1(1 + x + · · · + x )j are proposed. Useful properties, such as recursion relations, symmetries and limiting theorems of the
A Semi-Infinite Construction of Unitary N=2 Modules
• Mathematics
• 2000
We show that each unitary representation of the N=2 superVirasoro algebra can be realized in terms of collective excitations'' over a filled Dirac sea of fermionic operators satisfying a
Bailey flows and Bose Fermi identities for the conformed coset models (A_1^(1))_N x (A_1^(1))_N' / (A_1^(1))_N+N'
• Mathematics
• 1997
We use the recently established higher-level Bailey lemma and Bose–Fermi polynomial identities for the minimal models M(p, p) to demonstrate the existence of a Bailey flow from M(p, p) to the coset
Integrable Sl 2 -modules as Infinite Tensor Products
• Mathematics
Absrtact. In this paper we develop an ideas and methods from [1]. Using the fusion product of the representations of the Lie algebra sl 2 , we construct a set of the integrable highest weight sl
On some special families of $q$-hypergeometric Maass forms
• Mathematics
• 2016
Using special polynomials introduced by Hikami and the second author in their study of torus knots, we construct classes of $q$-hypergeometric series lying in the Habiro ring. These give rise to new

## References

SHOWING 1-10 OF 60 REFERENCES
On the combinatorics of row and corner transfer matrices of the $A_n-1^(1)$ restricted face models
We establish a weight-preserving bijection between the index sets of the spectral data of row-to-row and corner transfer matrices for $U_q\widehat{sl(n)}$ restricted interaction round a face (IRF)
Fermionic solution of the Andrews-Baxter-Forrester model. II. Proof of Melzer's polynomial identities
AbstractWe compute the one-dimensional configuration sums of the ABF model using the fermionic technique introduced in part I of this paper. Combined with the results of Andrews, Baxter, and
Dilogarithm identities
We study the dilogarithm identities from algebraic, analytic, asymptotic, $K$-theoretic, combinatorial and representation-theoretic points of view. We prove that a lot of dilogarithm identities
FERMIONIC CHARACTER SUMS AND THE CORNER TRANSFER MATRIX
We present a "natural finitization" of the fermionic q-series (certain generalizations of the Rogers–Ramanujan sums) which were recently conjectured to be equal to Virasoro characters of the unitary
Fermionic solution of the Andrews-Baxter-Forrester model. I. Unification of TBA and CTM methods
The problem of computing the one-dimensional configuration sums of the ABF model in regime III is mapped onto the problem of evaluating the grandcanonical partition function of a gas of charged
Exceptional structure of the dilute A(3) model: E(8) and E(7) Rogers-Ramanujan identities
• Mathematics
• 1994
The dilute A3 lattice model in regime 2 is in the universality class of the Ising model in a magnetic field. Here we directly establish the existence of an E8 structure in the dilute A3 model in this