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- Title
- Categorical crystals for quantum affine algebras
- KIAS Author
- Kashiwara, Masaki
- Journal
- JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 2022
- Archive
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- Abstract
- In this paper, a new categorical crystal structure for the quantum affine algebras is presented. We introduce the notion of extended crystals (B) over cap (g)(infinity) for an arbitrary quantum group U-q(g), which is the product of infinite copies of the crystal B(infinity) For a complete duality datum D in the Hernandez-Leclerc category C-g(0) of a quantum affine algebra U'(q)(g), we prove that the set B-D(g) of the isomorphism classes of simple modules in C-g(0) has an extended crystal structure isomorphic to (B) over cap (gfin)(infinity). An explicit combinatorial description of the extended crystal B-D(g) for affine type A(n)((1)) is given in terms of affine highest weights.