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Medientyp:
E-Artikel
Titel:
VI-modules in non-describing characteristic, part II
Beteiligte:
Nagpal, Rohit
Erschienen:
Walter de Gruyter GmbH, 2021
Erschienen in:Journal für die reine und angewandte Mathematik (Crelles Journal)
Sprache:
Englisch
DOI:
10.1515/crelle-2021-0054
ISSN:
0075-4102;
1435-5345
Entstehung:
Anmerkungen:
Beschreibung:
<jats:title>Abstract</jats:title>
<jats:p>We classify all irreducible generic <jats:inline-formula id="j_crelle-2021-0054_ineq_9999">
<jats:alternatives>
<m:math xmlns:m="http://www.w3.org/1998/Math/MathML">
<m:mi>VI</m:mi>
</m:math>
<jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_crelle-2021-0054_eq_0435.png" />
<jats:tex-math>{\mathrm{VI}}</jats:tex-math>
</jats:alternatives>
</jats:inline-formula>-modules in non-describing characteristic.
Our result degenerates to yield a classification of irreducible generic <jats:inline-formula id="j_crelle-2021-0054_ineq_9998">
<jats:alternatives>
<m:math xmlns:m="http://www.w3.org/1998/Math/MathML">
<m:mi>FI</m:mi>
</m:math>
<jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_crelle-2021-0054_eq_0401.png" />
<jats:tex-math>{\mathrm{FI}}</jats:tex-math>
</jats:alternatives>
</jats:inline-formula>-modules in arbitrary characteristic. Equivalently, we provide a complete classification of irreducibles of admissible <jats:inline-formula id="j_crelle-2021-0054_ineq_9997">
<jats:alternatives>
<m:math xmlns:m="http://www.w3.org/1998/Math/MathML">
<m:mrow>
<m:msub>
<m:mi>𝐆𝐋</m:mi>
<m:mi mathvariant="normal">∞</m:mi>
</m:msub>
<m:mo></m:mo>
<m:mrow>
<m:mo stretchy="false">(</m:mo>
<m:msub>
<m:mi>𝔽</m:mi>
<m:mi>q</m:mi>
</m:msub>
<m:mo stretchy="false">)</m:mo>
</m:mrow>
</m:mrow>
</m:math>
<jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_crelle-2021-0054_eq_0337.png" />
<jats:tex-math>{\mathbf{GL}_{\infty}(\mathbb{F}_{q})}</jats:tex-math>
</jats:alternatives>
</jats:inline-formula>-representations in non-describing characteristic, which is new even in characteristic zero. This result degenerates to provide a complete classification of irreducibles of admissible <jats:inline-formula id="j_crelle-2021-0054_ineq_9996">
<jats:alternatives>
<m:math xmlns:m="http://www.w3.org/1998/Math/MathML">
<m:msub>
<m:mi>S</m:mi>
<m:mi mathvariant="normal">∞</m:mi>
</m:msub>
</m:math>
<jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_crelle-2021-0054_eq_0227.png" />
<jats:tex-math>{S_{\infty}}</jats:tex-math>
</jats:alternatives>
</jats:inline-formula>-representations in arbitrary characteristic, which is new away from characteristic zero.</jats:p>