On the Induction of p-Cells

Lars Thorge Jensen; Leonardo Patimo

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arXiv · 1911.08969

On the Induction of p-Cells

Lars Thorge Jensen·Leonardo Patimo

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Abstract

We study cells with respect to the $p$-canonical basis of the Hecke algebra of a crystallographic Coxeter system (see arXiv:1510.01556, arXiv:1901.02323) 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.

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Lars Thorge Jensen, Leonardo Patimo. 2019-11-20. On the Induction of p-Cells. https://arxiv.org/abs/1911.08969

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