Crystal Bases for Quantum Generalized Kac–Moody Algebras

By Kyeonghoon Jeong, Seok-Jin Kang, Masaki Kashiwara. 2003

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In this paper, we develop the crystal basis theory for quantum generalized Kac–Moody algebras. For a quantum generalized Kac–Moody algebra Uq(g), we first introduce the category Oint of Uq(g)‐modules and prove its semisimplicity. Next, we define the notion of crystal bases for Uq(g)‐modules in the category Oint and for the subalgebra Uq−(g) . We then prove the tensor product rule and the existence theorem for crystal bases. Finally, we construct the global bases for Uq(g)‐modules in the category Oint and for the subalgebra Uq−(g) . 2000 Mathematics Subject Classification 17B37, 17B67.

Subfields: Algebra and Number Theory, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/105280cd29685f4ea005f9c06bcd159c8e5bde40