Sarah Brauner, Tamar Friedmann
Published 2018-03-29, updated 2021-01-19Version 2
We simplify a dual straightening algorithm which gives a presentation of Specht modules as a quotient of the space of column tabloids by dual Garnir relations. We show that this presentation can be generated by a single relation for each pair of columns of a tableau with ordered columns, thereby significantly reducing the number of generators given in the original construction. Our presentation applies to all Specht modules, and is of a similar nature to a recent result by Friedmann-Hanlon-Stanley-Wachs that applies to staircase partitions. We then discuss applications of our simplified presentation to a generalization of the multilinear component of the free Lie algebra studied by Friedmann, Hanlon, Stanley and Wachs.
Comments: Fixed mistake in Theorem 2.5. Section 3 has been rewritten to better reflect motivation, and all technical details have been moved to an appendix. Previous appendix has been removed
The construction of a class of presentations for Specht modules
The plethystic inverse of the odd Lie representations $Lie_{2n+1}$
A web basis of invariant polynomials from noncrossing partitions
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