Crystal Bases as Tuples of Integer Sequences. (10th June 2013)

• Record Type: Journal Article
• Authors: Kus, Deniz
• Other Names: Caramia M. Academic Editor.; Dondi R. Academic Editor.
• Is Part Of: ISRN combinatorics. Volume 2013(2013)
• Publication Date: 2013-06-10
• Subjects: Combinatorial analysis -- Periodicals; Combinatorial analysis; Electronic journals; Periodicals; 511.6
• DOI: 10.1155/2013/431024
• Languages: English
• ISSNs: 2090-8911

Abstract

Abstract : We describe a set ℛ ∞ consisting of tuples of integer sequences and provide certain explicit maps on it. We show that this defines a semiregular crystal for 𝔰 𝔩 n + 1 and 𝔰 𝔭 2 n, respectively. Furthermore, we define for any dominant integral weight λ a connected subcrystal ℛ ( λ ) in ℛ ∞, such that this crystal is isomorphic to the crystal graph B ( λ ) . Finally, we provide an explicit description of these connected crystals ℛ ( λ ) .