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Involutions on pro-𝑝-Iwahori Hecke algebras
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| Zeitschriftentitel: | Representation Theory of the American Mathematical Society |
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| Personen und Körperschaften: | |
| In: | Representation Theory of the American Mathematical Society, 23, 2019, 2, S. 57-87 |
| Format: | E-Article |
| Sprache: | Englisch |
| veröffentlicht: |
American Mathematical Society (AMS)
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| Schlagwörter: |
| Zusammenfassung: | <p>The pro-<inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="p"> <mml:semantics> <mml:mi>p</mml:mi> <mml:annotation encoding="application/x-tex">p</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-Iwahori Hecke algebra has an involution <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="iota"> <mml:semantics> <mml:mi>ι<!-- ι --></mml:mi> <mml:annotation encoding="application/x-tex">\iota</mml:annotation> </mml:semantics> </mml:math> </inline-formula> defined in terms of the Iwahori-Matsumoto basis. Then for a module <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="pi"> <mml:semantics> <mml:mi>π<!-- π --></mml:mi> <mml:annotation encoding="application/x-tex">\pi</mml:annotation> </mml:semantics> </mml:math> </inline-formula> of pro-<inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="p"> <mml:semantics> <mml:mi>p</mml:mi> <mml:annotation encoding="application/x-tex">p</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-Iwahori Hecke, <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="pi Superscript iota Baseline equals pi ring iota"> <mml:semantics> <mml:mrow> <mml:msup> <mml:mi>π<!-- π --></mml:mi> <mml:mi>ι<!-- ι --></mml:mi> </mml:msup> <mml:mo>=</mml:mo> <mml:mi>π<!-- π --></mml:mi> <mml:mo>∘<!-- ∘ --></mml:mo> <mml:mi>ι<!-- ι --></mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">\pi ^\iota = \pi \circ \iota</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is also a module. We calculate <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="pi Superscript iota"> <mml:semantics> <mml:msup> <mml:mi>π<!-- π --></mml:mi> <mml:mi>ι<!-- ι --></mml:mi> </mml:msup> <mml:annotation encoding="application/x-tex">\pi ^\iota</mml:annotation> </mml:semantics> </mml:math> </inline-formula> for simple modules <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="pi"> <mml:semantics> <mml:mi>π<!-- π --></mml:mi> <mml:annotation encoding="application/x-tex">\pi</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. We also calculate the dual of <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="pi"> <mml:semantics> <mml:mi>π<!-- π --></mml:mi> <mml:annotation encoding="application/x-tex">\pi</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. These calculations will be used for calculating the extensions between simple modules.</p> |
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| Umfang: | 57-87 |
| ISSN: |
1088-4165
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| DOI: | 10.1090/ert/521 |