Toric Degenerations and tropical geometry of branching algebras

Abstract

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.

11 figures; shortened

References in corpus (4)

• Reciprocity Algebras and Branching for Classical Symmetric Pairs
• The projective invariants of ordered points on the line
• Presentations of Semigroup Algebras of Weighted Trees
• Okounkov bodies and toric degenerations

Cited by in corpus (6)

• The $m-$dissimilarity map and representation theory of $S{L}_m$
• Semigroups of $s{l}_3(\mathbb{C})$ tensor product invariants
• Integrable systems, toric degenerations and Okounkov bodies
• Cox rings of moduli of quasi parabolic principal bundles and the K-Pieri rule
• Faithful tropicalization of the Grassmannian of planes
• Newton-Okounkov polyhedra for character varieties and configuration spaces