The canonical basis and the quantum Frobenius morphism

Details The canonical basis and the quantum Frobenius morphism The canonical basis and the quantum Frobenius morphism

2011-12-31

arxiv.org/abs/1201.0303v2

Mathematics

Representation Theory

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Scientific paper

The first goal of this paper is to study the amount of compatibility between two important constructions in the theory of quantized enveloping algebras, namely the canonical basis and the quantum Frobenius morphism. The second goal is to study orders with which the Kashiwara crystal B(infinity) of a symmetrizable Kac-Moody algebra can be endowed; these orders are defined so that the transition matrices between bases naturally indexed by B(infinity) are lower triangular.

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