Crystal duality and Littlewood-Richardson rule of extremal weight crystals

Details Crystal duality and Littlewood-Richardson rule of extremal weight crystals Crystal duality and Littlewood-Richardson rule of extremal weight crystals

2009-09-07

arxiv.org/abs/0909.1126v2

Mathematics

Quantum Algebra

Scientific paper

We consider a category of $\gl_\infty$-crystals, whose objects are disjoint unions of extremal weight crystals of non-negative level with certain finite conditions on the multiplicity of connected components. We show that it is a monoidal category under tensor product of crystals and the associated Grothendieck ring is anti-isomorphic to an Ore extension of the character ring of integrable lowest weight $\gl_\infty$-modules with respect to derivations shifting the characters of fundamental modules. A Littlewood-Richardson rule of extremal weight crystals with non-negative level is described explicitly in terms of classical Littlewood-Richardson coefficients.

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