Dilogarithm identities
| dc.creator | Kirillov, Anatol N. | |
| dc.date | 1994-08-20 | |
| dc.date | 1994-08-25 | |
| dc.date.accessioned | 2026-07-07T11:14:44Z | |
| dc.date.available | 2026-07-07T11:14:44Z | |
| dc.description | 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 (hypothetically all !) can be obtained by using the five-term relation only. Among those the Coxeter, Lewin, Loxton and Browkin ones are contained. Accessibility of Lewin's one variable and Ray's multivariable (here for $n\le 2$ only) functional equations is given. For odd levels the $\hat{sl_2}$ case of Kuniba-Nakanishi's dilogarithm conjecture is proven and additional results about remainder term are obtained. The connections between dilogarithm identities and Rogers-Ramanujan-Andrews-Gordon type partition identities via their asymptotic behavior are discussed. Some new results about the string functions for level $k$ vacuum representation of the affine Lie algebra $\hat{sl_n}$ are obtained. Connection between dilogarithm identities and algebraic $K$-theory (torsion in $K_3({\bf R})$) is discussed. Relations between crystal basis, branching functions $b_λ^{kΛ_0}(q)$ and Kostka-Foulkes polynomials (Lusztig's $q$-analog of weight multiplicity) are considered. The Melzer and Milne conjectures are proven. In some special cases we are proving that the branching functions $b_λ^{kΛ_0}(q)$ are equal to an appropriate limit of Kostka polynomials (the so-called Thermodynamic Bethe Ansatz limit). Connection between "finite-dimensional part of crystal base" and Robinson-Schensted-Knuth correspondence is considered. | |
| dc.description | 96 pages | |
| dc.identifier | https://arxiv.org/abs/hep-th/9408113 | |
| dc.identifier | http://arxiv.org/abs/hep-th/9408113 | |
| dc.identifier | Prog.Theor.Phys.Suppl.118:61-142,1995 | |
| dc.identifier | doi:10.1143/PTPS.118.61 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/192174 | |
| dc.subject | High Energy Physics - Theory | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | Quantum Algebra | |
| dc.title | Dilogarithm identities | |
| dc.type | text |