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2000•Birkhäuser Boston eBooksOpen access

The Bethe Equation at q = 0, the Möbius Inversion Formula, and Weight Multiplicities I: The sl (2) Case

Atsuo Kuniba, Tomoki Nakanishi

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Abstract

The \({{U}_{q}}(\widehat{{\mathfrak{s}\mathfrak{l}}}(2))\) Bethe equation is studied at q = 0. A linear congruence equation is proposed related to the string solutions. The number of its off-diagonal solutions is expressed in terms of an explicit combinatorial formula and coincides with the weight multiplicities of the quantum space. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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What this paper is about

The \({{U}_{q}}(\widehat{{\mathfrak{s}\mathfrak{l}}}(2))\) Bethe equation is studied at q = 0. A linear congruence equation is proposed related to the string solutions. The number of its off-diagonal solutions is expressed in terms of an explicit combinatorial formula and coincides with the weight multiplicities of the quantum space. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Available abstract

The \({{U}_{q}}(\widehat{{\mathfrak{s}\mathfrak{l}}}(2))\) Bethe equation is studied at q = 0. A linear congruence equation is proposed related to the string solutions. The number of its off-diagonal solutions is expressed in terms of an explicit combinatorial formula and coincides with the weight multiplicities of the quantum space. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Key concepts: Diagonal, Mathematics, Congruence (geometry), Mathematical physics, Pure mathematics, Geometry

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