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DTSTAMP:20260410T162654
DTSTART;TZID=America/Detroit:20260423T100000
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SUMMARY:Presentation:A Novel Construction for $\mathfrak{sl}_4$ Webs
DESCRIPTION:Abstract: The standard monomial basis for $\mathfrak{sl}_r$-invariant polynomials is indexed by rectangular standard Young tableaux\, but it lacks rotational invariance. Although promotion induces a cyclic action on tableaux\, a more symmetric basis is desirable. For $\mathfrak{sl}_2$ and $\mathfrak{sl}_3$\, such bases are given by non-crossing matchings and non-elliptic $\mathfrak{sl}_3$ webs\, respectively. In the case of $\mathfrak{sl}_4$\, a web basis has recently been constructed using hourglass plabic graphs\, but this approach relies on intricate growth rules and does not readily generalize to higher rank.\n\nIn this thesis\, we introduce a simpler and more direct construction of $\mathfrak{sl}_4$ webs. Starting from a rectangular four-row standard Young tableau\, we construct the associated web by stacking the $\mathfrak{sl}_3$ webs corresponding to the top three rows and the bottom three rows\, identifying along the non-crossing matching determined by the middle two rows. We prove that the resulting web is fully reduced and lies in the same equivalence class as the $\mathfrak{sl}_4$ web obtained via growth rules.
UID:147638-21901454@events.umich.edu
URL:https://events.umich.edu/event/147638
CLASS:PUBLIC
STATUS:CONFIRMED
CATEGORIES:Dissertation,Graduate,Graduate Students,Mathematics
LOCATION:East Hall - 3096
CONTACT:
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