# Paths, crystals and fermionic formulae

@inproceedings{Hatayama2001PathsCA, title={Paths, crystals and fermionic formulae}, author={Goro Hatayama and Atsuo Kuniba and Masato Okado and Taichiro Takagi and Zengo Tsuboi}, year={2001} }

We introduce a fermionic formula associated with any quantum affine algebra U q (X N (r) . Guided by the interplay between corner transfer matrix and the Bethe ansatz in solvable lattice models, we study several aspects related to representation theory, most crucially, the crystal basis theory. They include one-dimensional sums over both finite and semi-infinite paths, spinon character formulae, Lepowsky—Primc type conjectural formula for vacuum string functions, dilogarithm identities, Q…

## 132 Citations

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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…

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