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Toric Degenerations and tropical geometry of branching algebras

We construct polyhedral families of valuations on the branching algebra of a morphism of reductive groups. This establishes a connection between the combinatorial rules for studying a branching problem and the tropical geometry of the branching algebra. In the special case when the branching problem comes from the inclusion of a Levi subgroup or a diagonal subgroup, we use the dual canonical basis of Lusztig and Kashiwara to build toric deformations of the branching algebra.

preprint2012arXivOpen access
Christopher Manon
math.RTmath.AG
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Christopher Manon

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