Crystal bases as tuples of integer sequences (Q361580)

In this paper the author proves that for root systems of types A and C the direct sum \(\mathcal{R}^\infty\) of the sets of sequences of certain pairs of integers is a semiregular crystal. For any dominant integral weight \(\lambda\) a subcrystal \(\mathcal{R}(\lambda)\) is defined as a certain connected component of \(\mathcal{R}^\infty\). Then the main result states that \(\mathcal{R}(\lambda)\) is isomorphic to Kashiwara's crystal graph \(B(\lambda)\). The author also gives an explicit description of the connected subcrystals \(\mathcal{R}(\lambda)\).