Statement B Implies Statement A
Statement B Implies Statement A
This chapter recalls the use of the Schützenberger involution on Gelfand-Tsetlin patterns to prove that Statement B implies Statement A. These statements will be discussed two more times in the later chapters of the book. Chapter 18 reinterprets both Statements A and B in terms of crystals, and directly proves that the reinterpreted Statement B implies the reinterpreted Statement A in Theorem 18.2. Then Chapter 19 again reinterprets Statements A and B in a different context, and yet again directly proves that the reinterpreted Statement B implies the reinterpreted Statement A in Theorem 19.10. The current chapter shows that the Schützenberger involution qᵣ can be formulated in terms of operations on short Gelfand-Tsetlin patterns. To facilitate the inductive proof, relevant equations are used.
Keywords: crystal, Schützenberger involution, Gelfand-Tsetlin pattern, Statement B, Statement A
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.
