Edward Richmond
A combinatorial characterization of tight fusion frames.
Thu, 12/15/2011 - 15:01 — SomNambulAuthors: Edward Richmond, Kurt Luoto, Marcin Bownik
Subjects: Functional Analysis
AbstractIn this paper we give a combinatorial characterization of tight fusion frame
(TFF) sequences using Littlewood-Richardson skew tableaux. The equal rank case
has been solved recently by Casazza, Fickus, Mixon, Wang, and Zhou. Our
characterization does not have this limitation. We also develop some methods
for generating TFF sequences. The basic technique is a majorization principle
for TFF sequences combined with spatial and Naimark dualities. We use these
methods and our characterization to give necessary and sufficient conditions
which are satisfied by the first three highest ranks.- Read more
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Branching Schubert calculus and the Belkale-Kumar product on cohomology.
Mon, 09/07/2009 - 10:33 — SomNambulAuthors: Nicolas Ressayre, Edward Richmond
Subjects: Algebraic Geometry
AbstractIn 2006, Belkale and Kumar define a new product on the cohomology of flag
varieties and use this new product to give an improved solution to the
eigencone problem for complex reductive groups. In this paper, we give a
generalization of the Belkale-Kumar product to the branching Schubert calculus
setting. The study of Branching Schubert calculus attempts to understand the
induced map on cohomology of an equivariant embedding of flag varieties. The
main application of our work is a compact formulation of the solution to the
branching eigencone problem.Branching Schubert calculus and the Belkale-Kumar product on cohomology.
Mon, 09/07/2009 - 10:33 — SomNambulAuthors: Nicolas Ressayre, Edward Richmond
Subjects: Algebraic Geometry
AbstractIn 2006, Belkale and Kumar define a new product on the cohomology of flag
varieties and use this new product to give an improved solution to the
eigencone problem for complex reductive groups. In this paper, we give a
generalization of the Belkale-Kumar product to the branching Schubert calculus
setting. The study of Branching Schubert calculus attempts to understand the
induced map on cohomology of an equivariant embedding of flag varieties. The
main application of our work is a compact formulation of the solution to the
branching eigencone problem.
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