Classification of very cuspidal representations of \(\mathrm{GL}_m(D)\) (Q2328042)

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Classification of very cuspidal representations of \(\mathrm{GL}_m(D)\)
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    Classification of very cuspidal representations of \(\mathrm{GL}_m(D)\) (English)
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    9 October 2019
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    Let \(F\) stand for a non-archimedean local field with finite residue field. An element of the general linear group \(\mathrm{GL}_n(F)\) is called generic if it is minimal over \(F\) and generates field of degree \(n\) over \(F\). In the paper under the review, the author provides a classification of generic elements of an inner form \(\mathrm{G}\) of \(\mathrm{GL}_n(F)\). This enables the author to classify supercuspidal representations of \(\mathrm{G}\) induced from very cuspidal representations of certain open subgroups, defined in terms of generic elements. The classification provided generalizes the one of epipelagic supercuspidal representations of \(\mathrm{G}\).
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    non-Archimedean local field
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    central simple algebra
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    very cuspidal representation
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    simple type
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    endo-class
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    torsion degree
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    parametric degree
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    depth
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