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CAGE: Philadelphia Area Combinatorics and Alg. Geometry Seminar

Thursday, December 6, 2018 - 3:00pm

Tamar Friedmann

Haverford College


University of Pennsylvania


I will discuss a generalization of Lie algebras called a “LAnKe” that was inspired by a question from string theory. A special case of this generalization is the LATKe, or “Lie algebra of the third kind”, which fits particularly well with the timing of this talk, since “latke” also means “potato pancakes”, a favorite Hanukkah food. I will also discuss the free LATKe and free LAnKe, along with the action of the symmetric group on them. This discussion generalizes free Lie algebras and the known symmetric group module Lie(k). One sequence of symmetric group  modules that arises in this context contains Specht modules whose dimensions are the Catalan numbers, leading to a theorem named the “CataLAnKe theorem.” If time allows, I will also discuss new ways to present Specht modules that follow from the CataLAnKe result.