Construction of eigenfunctions for a system of quantum minors of the monodromy matrix for an SL(n,ℂ)-invariant spin chain View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2016-11

AUTHORS

P. A. Valinevich, S. É. Derkachov, P. P. Kulish, E. M. Uvarov

ABSTRACT

We consider the problem of seeking the eigenvectors for a commuting family of quantum minors of the monodromy matrix for an SL(n,ℂ)-invariant inhomogeneous spin chain. The algebra generators and elements of the L-operator at each site of the chain are implemented as linear differential operators in the space of functions of n(n−1)/2 variables. In the general case, the representation of the sln(ℂ) algebra at each site is infinite-dimensional and belongs to the principal unitary series. We solve this problem using a recursive procedure with respect to the rank n of the algebra. We obtain explicit expressions for the eigenvalues and eigenvectors of the commuting family. We consider the particular cases n = 2 and n = 3 and also the limit case of the one-site chain in detail. More... »

PAGES

1529-1553

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1134/s0040577916110015

DOI

http://dx.doi.org/10.1134/s0040577916110015

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1006266616


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