Crystal Bases as Tuples of Integer Sequences. (10th June 2013) - Kus, Deniz
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 ) .