Algebra Seminar: Gibson -- A Demazure Character formula for the product monomial crystal, and connections to generalised Schur modules

Joel Gibson (University of Sydney) 

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

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

Abstract: 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.