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Typical representations of admissible type I algebraic supergroups
Abstract
We study typical representations of an admissible type I algebraic supergroup G. We prove that, for a dominant weight λ, the induced supermodule H0G(λ) is simple if and only if λ is typical and the induced module H0Gev(λ) for the even subgroup Gev is simple. We establish equivalences between typical blocks for G and blocks for Gev, and give a projectivity criterion for Kac modules over every Frobenius kernel. For connected SpO(2ℓ|2) over an algebraically closed field of odd characteristic, we classify all simple projective supermodules over Frobenius kernels.
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BibTeX
@misc{shibata2026typical,
title = {{Typical representations of admissible type I algebraic supergroups}},
author = {Taiki Shibata},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.23055},
eprint = {2610.23055},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.23055},
}
RIS
TY - UNPB
TI - Typical representations of admissible type I algebraic supergroups
AU - Taiki Shibata
PY - 2026
DA - 2026/10/16
PB - arXiv
DO - 10.48550/arxiv.2610.23055
UR - https://arxiv.org/abs/2610.23055
AB - We study typical representations of an admissible type I algebraic supergroup G. We prove that, for a dominant weight λ, the induced supermodule H^0_G(λ) is simple if and only if λ is typical and the induced module H^0_G_ev(λ) for the even subgroup G_ev is simple. We establish equivalences between typical blocks for G and blocks for G_ev, and give a projectivity criterion for Kac modules over every Frobenius kernel. For connected SpO(2ℓ|2) over an algebraically closed field of odd characteristic, we classify all simple projective supermodules over Frobenius kernels.
ER -