Cyclotomic Gaudin models: construction and Bethe ansatz

Benoit Vicedo, Charles A. S. Young

    Research output: Contribution to journalArticlepeer-review

    10 Citations (Scopus)
    55 Downloads (Pure)

    Abstract

    To any simple Lie algebra $\mathfrak g$ and automorphism $\sigma:\mathfrak g\to \mathfrak g$ we associate a cyclotomic Gaudin algebra. This is a large commutative subalgebra of $U(\mathfrak g)^{\otimes N}$ generated by a hierarchy of cyclotomic Gaudin Hamiltonians. It reduces to the Gaudin algebra in the special case $\sigma = \text{id}$. We go on to construct joint eigenvectors and their eigenvalues for this hierarchy of cyclotomic Gaudin Hamiltonians, in the case of a spin chain consisting of a tensor product of Verma modules. To do so we generalize an approach to the Bethe ansatz due to Feigin, Frenkel and Reshetikhin involving vertex algebras and the Wakimoto construction. As part of this construction, we make use of a theorem concerning cyclotomic coinvariants, which we prove in a companion paper. As a byproduct, we obtain a cyclotomic generalization of the Schechtman-Varchenko formula for the weight function.
    Original languageEnglish
    Pages (from-to)971-1024
    Number of pages53
    JournalCommunications in Mathematical Physics
    Volume343
    Issue number3
    Early online date24 Mar 2016
    DOIs
    Publication statusPublished - 22 Apr 2016

    Keywords

    • math.QA

    Fingerprint

    Dive into the research topics of 'Cyclotomic Gaudin models: construction and Bethe ansatz'. Together they form a unique fingerprint.

    Cite this