A path model for geodesics in Euclidean buildings and its applications to representation theory
By Michael Kapovich, John Millson. 2004
75 citations recorded by the source corpus.
In this paper we give a combinatorial characterization of projections of geodesics in Euclidean buildings to Weyl chambers. We apply these results to the representation theory of complex reductive Lie groups and to spherical Hecke rings associated with split nonar- chimedean reductive Lie groups. Our main application is a generalization of the saturation theorem of Knutson and Tao for SLn to other complex semisimple Lie groups.
Subfields: Computer Graphics and Computer-Aided Design, Discrete Mathematics and Combinatorics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/41f3295566e6e2b9c5c4bbd47807db7475415719
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In Computer Graphics and Computer-Aided Design
In Discrete Mathematics and Combinatorics
In Geometry and Topology
Citations in the corpus
- Galleries, Hall-Littlewood polynomials, and structure constants of the spherical Hecke algebra (2005, methodology): “In [KM04] a similar formula for C λμ with some restrictions on λ, μ, ν was given by Kapovich and Millson using geodesic triangles in some euclidean building associated to the situation.”
- Alcove Walks, Hecke Algebras, Spherical Functions, Crystals and Column Strict Tableaux (2006, methodology): “e case (projecting onto the line perpendicular to Hα). More importantly, the definition of the product ⊗is forced by (4.28-4.30). The following theorem is a version of [Sc, Theorem 1.2] and results in [KM] and [Ha]. Theorem 4.9. Recall the notations from Theorem 4.2. If λ ∈P+ let Bq(pλ) be the q-crys”