The many faces of a character

1993/12/06 by Ezer Melzer · 5 citations
Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Affine transformation #Algebra over a field #Algebraic structures and combinatorial models #Character (mathematics) #Conjecture #Integrable system #Limit (mathematics) #Macdonald polynomials #Random Matrices and Applications #Representation (politics) #hep-th

paper · pdf · doi:10.1007/bf00761715

published as Lett.Math.Phys. 31 (1994) 233-246 · 14/9 pages in harvmac, Tel-Aviv preprint TAUP 2125-93

arxiv created 1993/12/06 · openalex publication_date 1994/07/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We prove an identity between three infinite families of polynomials which are defined in terms of `bosonic', `fermionic', and `one-dimensional configuration' sums. In the limit where the polynomials become infinite series, they give different-looking expressions for the characters of the two integrable representations of the affine su(2) algebra at level one. We conjecture yet another fermionic sum representation for the polynomials which is constructed directly from the Bethe-Ansatz solution of the Heisenberg spin chain.

Citations

• Infinite conformal symmetry in two-dimensional quantum field theory
• FERMIONIC CHARACTER SUMS AND THE CORNER TRANSFER MATRIX

Cited by

• Multinomials and polynomial bosonic forms for the branching functions of the (2) x (2)/(2) conformal coset models
• Character expansion for HOMFLY polynomials. II. Fundamental representation. Up to five strands in braid
• Spinons in magnetic chains of arbitrary spins at finite temperatures
• Physical combinatorics and quasiparticles
• Path representation of suˆ(2)k states I: Operators and particles for k=1,2