A gallery model for affine flag varieties

Positively folded galleries in Coxeter complexes play a role in many areas of maths, such as in the study of affine Hecke algebras, Macdonald polynomials, MV-polytopes, and affine Deligne-Lusztig varieties.

In this talk, we will define positively folded galleries, and then look at a new recursive description of the set of end alcoves of folded galleries which are positive with respect to alcove-induced orientations. This further allow us to find the images of retractions from certain points at infinity, giving us a combinatorial description of double coset intersections in the affine flag variety. This talk is based on joint work with Elizabeth Milićević, Petra Schwer and Anne Thomas.  

About the speaker

Dr Yusra Naqvi is a postdoc in Mathematics at the University of Sydney. She received her PhD from Rutgers University under the supervision of Siddhartha Sahi.