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DilogarithmIdentities Anatol N. Kirillov1995 год

Dilogarithm Identities
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Аннотация: 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 from n ≤2 only) functional equations is given. For odd levels and case of Kuniba-Nakanishi's dilogarithm conjecture is proven and additional results about remainder them 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 are obtained. Connection between dilogarithm identities and algebraic K-theory (torsion in K3(R)) is discussed. Relations between crystal bases, branching functions bλkΛ0(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 bλkΛ0(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.
Год издания: 1995
Авторы: Anatol N. Kirillov
Издательство: Oxford University Press
Источник: Progress of Theoretical Physics Supplement
Ключевые слова: Advanced Mathematical Identities, Advanced Combinatorial Mathematics, Algebraic structures and combinatorial models
Другие ссылки: Progress of Theoretical Physics Supplement (PDF)
Progress of Theoretical Physics Supplement (HTML)
arXiv (Cornell University) (PDF)
arXiv (Cornell University) (HTML)
DataCite API (HTML)