Abstract
For a split quasireductive supergroup \(\mathbbm {G}\) defined over a field, we study structure and representation of Frobenius kernels \(\mathbbm {G}_r\) of \(\mathbbm {G}\) and we give a necessary and sufficient condition for \(\mathbbm {G}_r\) to be unimodular in terms of the root system of \(\mathbbm {G}\). We also establish Steinberg’s tensor product theorem for \(\mathbbm {G}\) under some natural assumptions.
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Acknowledgements
The author thanks the anonymous referees for their helpful comments that improved the quality of the manuscript. The author is supported by JSPS KAKENHI Grant Numbers JP19K14517 and JP22K13905.
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The author is supported by JSPS KAKENHI Grant Numbers JP19K14517 and JP22K13905.
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Presented by: Michel Brion
Dedicated to Professor Akira Masuoka on the occasion of his 60th birthday.
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Shibata, T. Frobenius Kernels of Algebraic Supergroups and Steinberg’s Tensor Product Theorem. Algebr Represent Theor 27, 927–959 (2024). https://doi.org/10.1007/s10468-023-10240-y
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DOI: https://doi.org/10.1007/s10468-023-10240-y