Abstract
Abstract We show that certain modular induced representations of GL 2 ⢠( F q ) \mathrm{GL}_{2}(\mathbb{F}_{q}) can be written as cokernels of operators acting on symmetric power representations of GL 2 ⢠( F q ) \mathrm{GL}_{2}(\mathbb{F}_{q}) . When the induction is from the Borel subgroup or the anisotropic torus, the operators involve multiplication by newly defined twisted Dickson polynomials or twisted Serre operators, respectively. Our isomorphisms are explicitly defined using differential operators. As a corollary, we improve some periodicity results for quotients in the theta filtration.
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