University of Sydney Algebra Seminar

Joel Gibson (University of Sydney)

Friday 17 May, 12-1pm, Place: Carslaw 375

A Demazure Character formula for the product monomial crystal, and connections to generalised Schur modules

All irreducible representations of a complex semisimple simply-laced Lie algebra arise geometrically as the homology of Nakajima quiver varieties. By considering certain generic torus actions on these quiver varieties, Nakajima also showed that tensor products of irreducible representations can be constructed in this way. However, there is very little explicitly known about the representations (and their crystals) which arise when this torus action is non-generic. In this talk, I will describe how the crystal arising from this action can be understood, leading to a Demazure-type character formula for the crystals (and therefore representations) arising from these torus actions. I will also describe the specific case of type A, where (perhaps surprisingly) these representations are isomorphic to generalised Schur modules.