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Garnir modules, their free resolutions, and Hall-Littlewood polynomials

Algebra & Discrete Mathematics

Speaker: Alexander Woo, UC Davis
Location: 693 Kerr
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".