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STUDY OF PARITY SHEAVES ARISING FROM GRADED LIE ALGEBRAS

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Let G be a complex, connected, reductive, algebraic group, and χ : ℂ× → G be a fixed cocharacter that defines a grading on \( \mathfrak{g} \), the Lie algebra of G. Let G0 be the centralizer of χ(ℂ×). In this paper, we study G0-equivariant parity sheaves on \( \mathfrak{g} \)n, under some assumptions on the field 𝕜 and also assuming two conjectures for the group G. However, both the conjectures are known in characteristic 0 and second conjecture holds for GLn in any characteristic. This paper uses results from Lusztig[Lu] in characteristic 0 and extends the results in positive characteristic. The main result is that every parity sheaf occurs as a direct summand of the parabolic induction of some cuspidal pair. The results are conditional on the conjectures.

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  1. Department of Mathematics, University of Georgia, Athens, GA, 30602, USA

    TAMANNA CHATTERJEE

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Dedicated to my father, Kishan Chatterjee

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Tamanna Chatterjee is supported by NSF grant.

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CHATTERJEE, T. STUDY OF PARITY SHEAVES ARISING FROM GRADED LIE ALGEBRAS. Transformation Groups 28, 591–637 (2023). https://doi.org/10.1007/s00031-023-09803-6

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