RSK type correspondence of Pictures and Littlewood-Richardson Crystals
Toshiki Nakashima, Miki Shimojo
TL;DR
This paper introduces a novel RSK-type correspondence linking pictures with pairs of Littlewood-Richardson crystals, expanding combinatorial representation theory.
Contribution
It establishes a new bijection between pictures and Littlewood-Richardson crystals, enhancing understanding of their combinatorial structures.
Findings
Established a one-to-one correspondence between pictures and pairs of crystals.
Provided a combinatorial framework connecting pictures with Littlewood-Richardson crystals.
Expanded the toolkit for studying crystal bases and their combinatorial representations.
Abstract
We present a Robinson-Schensted-Knuth type one-to-one correspondence between the set of pictures and the set of pairs of Littlewood-Richardson crystals.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Combinatorial Mathematics · Advanced Algebra and Geometry