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Stability and Combinatorics of plethysm
Algebra & Discrete Mathematics| Speaker: | Chris Bowman, University of York |
| Related Webpage: | https://sites.google.com/site/chrisdbowman40/home?authuser=0 |
| Location: | 2112 MSB |
| Start time: | Tue, May 7 2024, 11:00AM |
This talk focuses on the decomposition of plethysm products of Schur functions, or equivalently of (induced) representations for symmetric groups, or certain natural modules (e.g. symmetric powers of symmetric powers) of the general linear group. Understanding these decompositions is an age-old combinatorial problem, made more tractable by the beautiful stability properties that these products exhibit. In this talk we discuss how diagrammatics can be used to provide new closed formulas for these (stable) decompositions. This generalises a famous formula of Manivel.