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October 15, 2025Open Access

An explicit decomposition of higher Deligne-Lsuztig representations

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The study reveals that the geometric analog of the Weil-Heisenberg representation differs by a quadratic character.
Under conditions on the residue field's cardinality, it establishes an explicit irreducible decomposition of elliptic higher Deligne-Lusztig representations.
The results imply that unramified Yu types are present in the cohomology of higher Deligne-Lusztig varieties.
Kaletha's regular supercuspidal representation can be derived from a higher Deligne-Lusztig representation with a sign adjustment.

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This note shows a relation between geometric analogs of Weil-Heisenberg representations and Yu types, indicating a new irreducible decomposition.

Liu et al. (2025) studied this question.

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This note shows a relation between geometric analogs of Weil-Heisenberg representations and Yu types, indicating a new irreducible decomposition.