We define a filtration by DG-subcategories on the DG-category Shv(Bun_G) of sheaves on the moduli of G-torsors on a curve, which is stable under the action of Hecke functors. We formulate a conjecture relating this filtration with another filtration on the spectral side of the categorical geometric Langlands conjecture. We also formulate a conjectural compatibility with the parabolic induction.
Some results on reducibility of parabolic induction for classical groups
Parabolic induction, categories of representations and operator spaces
A filtration on rings of representations of non-Archimedean $GL_n$
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