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Involutions on pro-𝑝-Iwahori Hecke algebras

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Zeitschriftentitel: Representation Theory of the American Mathematical Society
Personen und Körperschaften: Abe, Noriyuki
In: Representation Theory of the American Mathematical Society, 23, 2019, 2, S. 57-87
Format: E-Article
Sprache: Englisch
veröffentlicht:
American Mathematical Society (AMS)
Schlagwörter:
Mathematics (miscellaneous)
author_facet Abe, Noriyuki
Abe, Noriyuki
author Abe, Noriyuki
spellingShingle Abe, Noriyuki
Representation Theory of the American Mathematical Society
Involutions on pro-𝑝-Iwahori Hecke algebras
Mathematics (miscellaneous)
author_sort abe, noriyuki
spelling Abe, Noriyuki 1088-4165 American Mathematical Society (AMS) Mathematics (miscellaneous) http://dx.doi.org/10.1090/ert/521 <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> Involutions on pro-𝑝-Iwahori Hecke algebras Representation Theory of the American Mathematical Society
doi_str_mv 10.1090/ert/521
facet_avail Online
Free
finc_class_facet Mathematik
format ElectronicArticle
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id ai-49-aHR0cDovL2R4LmRvaS5vcmcvMTAuMTA5MC9lcnQvNTIx
institution DE-14
DE-105
DE-Ch1
DE-L229
DE-D275
DE-Bn3
DE-Brt1
DE-Zwi2
DE-D161
DE-Zi4
DE-Gla1
DE-15
DE-Pl11
DE-Rs1
imprint American Mathematical Society (AMS), 2019
imprint_str_mv American Mathematical Society (AMS), 2019
issn 1088-4165
issn_str_mv 1088-4165
language English
mega_collection American Mathematical Society (AMS) (CrossRef)
match_str abe2019involutionsonpropyogiwahoriheckealgebras
publishDateSort 2019
publisher American Mathematical Society (AMS)
recordtype ai
record_format ai
series Representation Theory of the American Mathematical Society
source_id 49
title Involutions on pro-𝑝-Iwahori Hecke algebras
title_unstemmed Involutions on pro-𝑝-Iwahori Hecke algebras
title_full Involutions on pro-𝑝-Iwahori Hecke algebras
title_fullStr Involutions on pro-𝑝-Iwahori Hecke algebras
title_full_unstemmed Involutions on pro-𝑝-Iwahori Hecke algebras
title_short Involutions on pro-𝑝-Iwahori Hecke algebras
title_sort involutions on pro-𝑝-iwahori hecke algebras
topic Mathematics (miscellaneous)
url http://dx.doi.org/10.1090/ert/521
publishDate 2019
physical 57-87
description <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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author Abe, Noriyuki
author_facet Abe, Noriyuki, Abe, Noriyuki
author_sort abe, noriyuki
container_issue 2
container_start_page 57
container_title Representation Theory of the American Mathematical Society
container_volume 23
description <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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id ai-49-aHR0cDovL2R4LmRvaS5vcmcvMTAuMTA5MC9lcnQvNTIx
imprint American Mathematical Society (AMS), 2019
imprint_str_mv American Mathematical Society (AMS), 2019
institution DE-14, DE-105, DE-Ch1, DE-L229, DE-D275, DE-Bn3, DE-Brt1, DE-Zwi2, DE-D161, DE-Zi4, DE-Gla1, DE-15, DE-Pl11, DE-Rs1
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series Representation Theory of the American Mathematical Society
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spelling Abe, Noriyuki 1088-4165 American Mathematical Society (AMS) Mathematics (miscellaneous) http://dx.doi.org/10.1090/ert/521 <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> Involutions on pro-𝑝-Iwahori Hecke algebras Representation Theory of the American Mathematical Society
spellingShingle Abe, Noriyuki, Representation Theory of the American Mathematical Society, Involutions on pro-𝑝-Iwahori Hecke algebras, Mathematics (miscellaneous)
title Involutions on pro-𝑝-Iwahori Hecke algebras
title_full Involutions on pro-𝑝-Iwahori Hecke algebras
title_fullStr Involutions on pro-𝑝-Iwahori Hecke algebras
title_full_unstemmed Involutions on pro-𝑝-Iwahori Hecke algebras
title_short Involutions on pro-𝑝-Iwahori Hecke algebras
title_sort involutions on pro-𝑝-iwahori hecke algebras
title_unstemmed Involutions on pro-𝑝-Iwahori Hecke algebras
topic Mathematics (miscellaneous)
url http://dx.doi.org/10.1090/ert/521