Friday, November 05 | |
Algebra Seminar
Time: 14:30
Speaker: Khanh Nguyen Duc (Otto-von-Guericke-University Magdeburg) Title: "The relations between Littlewood-Richardson coefficients and its shifted version" Room: ZOOM (968 6609 0477) Abstract: We give a new interpretation of the shifted Littlewood-Richardson coefficients fνλμ (λ,μ,ν are strict partitions). The coefficients gλμ which appear in the decomposition of Schur Q-function Qλ into the sum of Schur functions Qλ=2l(λ)∑μgλμsμ can be considered as a special case of fνλμ (here λ is a strict partition of length l(λ)). We also give another description for gλμ as the cardinal of a subset of a set that counts Littlewood-Richardson coefficients c˜λμtμ. This new point of view allows us to establish connections between gλμ and c˜λμtμ. More precisely, we prove that gλμ=gλμt, and gλμ≤c˜λμtμ. We conjecture that g2λμ≤c˜λμtμ and formulate some conjectures on our combinatorial models which would imply this inequality if it is valid. We present an approach using Fomin diagrams and Viennot's geometric construction for RSK correspondence to attack the conjecture. | |
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