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Schubert cells and Whittaker functionals for GL ( r , R ) part I: Combinatorics
1Mathematisches Institut, Universität Bonn, Endenicher Allee 60, 53129 Bonn, Germany.
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We give a formula for a birational map on the Schubert cell associated to each Weyl group element of . 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 via integration by parts. In this paper, we establish combinatorial properties of the birational map and prove auxiliary results.
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