Alcove walks and spherical Whittaker functions

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Date

2021

Authors

Huynh, Matthew

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Abstract

Labeled minimal walks in the path model correspond bijectively with points of the affine flag variety G/I. By using the folding algorithm introduced in \cite{prs09}, we can use folded labeled walks to describe points of triple intersections UvIIwIU+vI in the affine flag variety. We demonstrate how to simplify the calculation of what steps can be folded, and use this to prove a result about the maximum number of folds allowed for a minimal walk. Finally, we explain how to compute the spherical Whittaker function using alcove walks following \cite{beaz13}, and for G=SL3 we prove a result about the alcove walks that contribute non-trivially to this computation.

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