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arXiv · 2410.13519

Schubert cells and Whittaker functionals for $\text{GL}(n,\mathbb{R})$ part I: Combinatorics

Doyon Kim
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Abstract

We give a formula for a birational map on the Schubert cell associated to each Weyl group element of $G=\text{GL}(n)$. 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 $\text{GL}(n,\mathbb{R})$ via integration by parts. In this paper, we establish combinatorial properties of the birational map and prove auxiliary results.

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BibTeXRIS

Doyon Kim. 2024-10-17. Schubert cells and Whittaker functionals for $\text{GL}(n,\mathbb{R})$ part I: Combinatorics. https://doi.org/10.1007/s00229-026-01726-2

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