2021/06/29 by Yael Karshon, Karshon, Yael, Jihyeon Jessie Yang +1
Mathematics · #22E46 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Representation Theory (math.RT) #Symplectic Geometry (math.SG)
paper · pdf · doi:10.48550/arxiv.2106.15695
openalex publication_date 2021/06/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Expanding an idea of Raoul Bott, we propose a construction of canonical bases for unitary representations that comes from big torus actions on families of Bott-Samelson manifolds. The construction depends only on the choices of a maximal torus, a Borel subgroup ,and a reduced expression for the longest element of the Weyl group. It relies on a conjectural vanishing of higher cohomology of sheaves of holomorphic sections of certain line bundles on the total spaces of the families, hence the question mark in the title.