Rigged configurations and the $$*$$-involution
نویسندگان
چکیده
منابع مشابه
Crystals and Rigged Configurations
Hatayama et al. conjectured fermionic formulas associated with tensor products of U ′ q (g)-crystals B. The crystals B correspond to the Kirillov–Reshetikhin modules which are certain finite dimensional U ′ q (g)-modules. In this paper we present a combinatorial description of the affine crystals Br,1 of type D n . A statistic preserving bijection between crystal paths for these crystals and ri...
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This note is a review of rigged configurations and the Bethe Ansatz. In the first part, we focus on the algebraic Bethe Ansatz for the spin 1/2 XXX model and explain how rigged configurations label the solutions of the Bethe equations. This yields the bijection between rigged configurations and crystal paths/Young tableaux of Kerov, Kirillov and Reshetikhin. In the second part, we discuss a gen...
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in terms of the crystal bases theory [K] and its application to the periodic box-ball systems following [S2] and [KS3]. The bijection φ was originally introduced in order to show the so-called X = M formula (see [O, S4] for reviews) by using its statistic preserving property. Recently, another application of the bijection φ to the box-ball systems [TS, T] was found [KOSTY]. In this context, the...
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There are (at least) two main approaches to solvable lattice models and their associated quantum spin chains: the Bethe ansatz [6] and the corner transfer matrix method [5]. In his paper [6], Bethe solved the Heisenberg spin chain based on the string hypothesis which asserts that the eigenvalues of the Hamiltonian form certain strings in the complex plane as the size of the system tends to infi...
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We give a review of the current status of the X = M conjecture. Here X stands for the one-dimensional configuration sum and M for the corresponding fermionic formula. There are three main versions of this conjecture: the unrestricted, the classically restricted and the level-restricted version. We discuss all three versions and illustrate the methods of proof with many examples for type A n−1. ...
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ژورنال
عنوان ژورنال: Letters in Mathematical Physics
سال: 2018
ISSN: 0377-9017,1573-0530
DOI: 10.1007/s11005-018-1063-2