arXiv subjects
Publications and source records attributed to Scott Larson.
We construct two categorifications of the Lusztig--Vogan module associated to a real reductive algebraic group. The first categorification is given by semisimple complexes in an equivariant derived category, and the second is constructed as a module category over Soergel bimodules. Our categorifications are related by taking equivariant hypercohomology.
We provide a method for gluing (small) resolutions of singularities of Schubert varieties \(X_w\). An explicit isomorphism of \(X_w\) with an (iterated) bundle is constructed when \(w\) has an (iterated) BP decomposition. Combined with the first result this gives many new small resolutions of Schubert varieties. In type A, this can be expressed in terms of pattern avoidance. Also we show resolutions of Schubert varieties constructed quite generally are in fact Gelfand-MacPherson resolutions.