2024/10/17 by Kim, Doyon
#05E14 (Secondary) #11F70 (Primary) #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.2410.13519
We give a formula for a birational map on the Schubert cell associated to each Weyl group element of G=GL(n). The map simplifies the UDL decomposition of matrices, providing structural insight into the Schubert cell decomposition of the flag variety G/B, where B is a Borel subgroup. An application of the formula includes a new proof of the existence of Whittaker functionals for principal series representations of GL(n,ℝ) via integration by parts. In this paper, we establish combinatorial properties of the birational map and prove auxiliary results.