# The Bailey Lemma and Kostka Polynomials

@article{Warnaar2002TheBL, title={The Bailey Lemma and Kostka Polynomials}, author={S. Warnaar}, journal={Journal of Algebraic Combinatorics}, year={2002}, volume={20}, pages={131-171} }

Using the theory of Kostka polynomials, we prove an An−1 version of Bailey's lemma at integral level. Exploiting a new, conjectural expansion for Kostka numbers, this is then generalized to fractional levels, leading to a new expression for admissible characters of A(1)n−1 and to identities for A-type branching functions.

#### 13 Citations

Bilateral Bailey lemma and Rogers-Ramanujan identities

- Mathematics, Computer Science
- Adv. Appl. Math.
- 2009

A bilateral Bailey lemma is proved and twenty-five transformation formulae between unilateral and bilateral summations for nonterminating basic hypergeometric series are established, including most of Slater's collection of 130 identities. Expand

Bailey Type Transforms and Applications

- Mathematics
- 2007

The aim of this paper is to establish new series transforms of Bailey type and to show that these Bailey type transforms work as efficiently as the classical one and give not only new… Expand

A U(n+1) Bailey lattice

- Mathematics
- 2015

Abstract Multiple basic hypergeometric series associated with the unitary group U ( n + 1 ) have been investigated by various authors. The purpose of this paper is to obtain a U ( n + 1 ) analogue of… Expand

New fermionic formula for unrestricted Kostka polynomials

- Computer Science, Mathematics
- J. Comb. Theory, Ser. A
- 2006

A new fermionic formula for the unrestricted Kostka polynomials of type An-1(1) is presented and is valid for all crystal paths based on Kirillov-Reshetikhin modules, not just for the symmetric and antisymmetric case. Expand

The Cn WP-Bailey chain

- Mathematics
- 2018

Abstract The purpose of this paper is to introduce the concept of Cn WP-Bailey pairs. The Cn WP-Bailey transform is obtained by applying the Cn6ϕ5 summation formula. From this result, the Cn… Expand

A ] 7 Ja n 20 07 BAILEY TYPE TRANSFORMS AND APPLICATIONS

- 2007

The aim of this paper is to establish new series transforms of Bailey type and to show that these Bailey type transforms work as efficiently as the c lassical one and give not only… Expand

Fermionic Formulas For Unrestricted Kostka Polynomials And Superconformal Characters

- Mathematics
- 2005

The problem of finding fermionic formulas for the many generalizations of Kostka polynomials and for the characters of conformal field theories has been a very exciting research topic for the last… Expand

NEW EXPLICIT EXPRESSION FOR A (1) SUPERNOMIALS

- Mathematics
- 2005

A new fermionic formula for type A (1) 1 supernomials is presented. This formula is different from the one given by Hatayama et al. (6). A new set of unrestricted rigged configurations is introduced… Expand

50 Years of Bailey’s Lemma

- Mathematics
- 2001

Half a century ago, The Proceedings of the London Mathematical Society published W. N. Bailey’s influential paper Identities of the Rogers-Ramanujan type [16]. The main result therein, which was… Expand

What the characters of irreducible subrepresentations of Jordan cells can tell us about LCFT

- Mathematics, Physics
- 2013

In this article, we review some aspects of logarithmic conformal field theories (LCFTs) which can be inferred from the characters of irreducible submodules of indecomposable modules. We will mainly… Expand

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