Garnir modules, their free resolutions, and Hall-Littlewood polynomialsAlgebra & Discrete Mathematics
|Speaker:||Alexander Woo, UC Davis|
|Start time:||Fri, Oct 21 2005, 1:10PM|
We consider certain modules of the polynomial ring C[x_1,...x_n] which arise naturally (in a specific way I will explain) from considering the symmetric group action permuting the variables. Conjecturally, the graded characters of these modules (considered as symmetric group representations) are Hall-Littlewood polynomials when interpreted as symmetric functions. Free resolutions of these modules seem to "explain" some formulas for and involving Hall-Littlewood polynomials.
All the symmetric function theory and commutative algebra needed for this talk will be developed "from scratch".