Transitioning between the tableaux and spider bases for the Specht modules

event Friday, April 17, 2020
access_time 3:30 PM
room Zoom
info Zoom link: https://oklahoma.zoom.us/j/577510951?pwd=bTRQQm9IcFJwMkFsRmpqcFJ2c0lhZz09

Abstract: The Specht modules admit a well-known polytabloid basis parametrized by standard Young tableaux of a fixed shape. On the other hand, classical invariant theory for sl_2 and s_3 suggests that these modules also admit a diagrammatical basis, which are Temperley-Lieb diagrams and Kuperberg spiders, for two types of Specht modules, respectively. It is natural to investigate the transitioning matrix between the tableaux basis and the web basis. We developed a combinatorial formula for computing entries in these matrices. Regarding these entries we proved a positivity conjecture for the Temperley-Lieb diagrams and a non-negativity result for the Kuperberg spiders.


For more information on this event, please contact Daniel Smolkin.