We study cells with respect to the p-canonical basis of the Hecke algebra of a crystallographic Coxeter system (see Jensen and Williamson (2017) and Jensen (2020)) and their compatibility with standard parabolic subgroups. We show that after induction to the surrounding bigger Coxeter group the cell module of a right p-cell in a standard parabolic subgroup decomposes as a direct sum of cell modules. Along the way, we state some new positivity properties of the p-canonical basis.
On the Induction of p-Cells
Patimo L.
2023-01-01
Abstract
We study cells with respect to the p-canonical basis of the Hecke algebra of a crystallographic Coxeter system (see Jensen and Williamson (2017) and Jensen (2020)) and their compatibility with standard parabolic subgroups. We show that after induction to the surrounding bigger Coxeter group the cell module of a right p-cell in a standard parabolic subgroup decomposes as a direct sum of cell modules. Along the way, we state some new positivity properties of the p-canonical basis.File in questo prodotto:
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