Crystals and Gelfand-Tsetlin Patterns
Crystals and Gelfand-Tsetlin Patterns
This chapter translates the definitions of the Weyl group multiple Dirichlet series into the language of crystal bases. It reinterprets the entries in these arrays and the accompanying boxing and circling rules in terms of the Kashiwara operators. Thus, what appeared as a pair of unmotivated functions on Gelfand-Tsetlin patterns in the previous chapter now takes on intrinsic representation theoretic meaning. The discussion is restricted to crystals of Cartan type Aᵣ. The Weyl vector, denoted by ρ, is considered as an element of the weight lattice, and the bijection between Gelfand-Tsetlin patterns and tableaux is described. The chapter also examines the λ-part of the multiple Dirichlet series in terms of crystal graphs.
Keywords: crystal base, Weyl group multiple Dirichlet series, Kashiwara operator, boxing, circling, Gelfand-Tsetlin pattern, crystal, Weyl vector, tableaux, crystal graph
Princeton Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.
Please, subscribe or login to access full text content.
If you think you should have access to this title, please contact your librarian.
To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us.
