Matrix Pairs over Valuation Rings and R-Valued Littlewood-Richardson Fillings

Details Matrix Pairs over Valuation Rings and R-Valued Littlewood-Richardson Fillings Matrix Pairs over Valuation Rings and R-Valued Littlewood-Richardson Fillings

2009-10-23

arxiv.org/abs/0910.4441v1

Mathematics

Combinatorics

39 pages

Scientific paper

We extend the theory of Littlewood-Richardson fillings (defined over the non-negative integers) to include diagrams with rows and boxes of real-valued length. We realize such fillings as invariants of matrix pairs over rings with a real-valued valuation. We then prove a bijection between pairs of fillings determined by a matrix pair, and connect this to the classical row-switching bijection for Littlewoo-Richardson fillings. We utilize matrix calculations to interpret continuous deformations of generalized Littlewood-Richardson fillings.

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