Perfect isometries and Murnaghan-Nakayama rules

This article is concerned with perfect isometries between blocks of finite groups. Generalizing a method of Enguehard to show that any two p-blocks of (possibly different) symmetric groups with the same weight are perfectly isometric, we prove analogues of this result for p-blocks of alternating gro...
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Autor*in:	Olivier Brunat [verfasserIn] Jean-Baptiste Gramain

Format:	Artikel
Sprache:	Englisch

Erschienen:	2017

Rechteinformationen:	Nutzungsrecht: © Copyright 2017, American Mathematical Society

Übergeordnetes Werk:	Enthalten in: Transactions of the American Mathematical Society - Providence, RI : American Mathematical Soc., 1900, 369(2017), 11, Seite 7657
Übergeordnetes Werk:	volume:369 ; year:2017 ; number:11 ; pages:7657

Links:	Volltext Link aufrufen

DOI / URN:	10.1090/tran/6860

Katalog-ID:	OLC199715546X

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allfields	10.1090/tran/6860 doi PQ20171228 (DE-627)OLC199715546X (DE-599)GBVOLC199715546X (PRQ)a654-1cb47f039bd09769251d316fd3c54b11a54ae20404239e3b68878c2a5d40fab00 (KEY)0042596620170000369001107657perfectisometriesandmurnaghannakayamarules DE-627 ger DE-627 rakwb eng 050 DE-101 510 AVZ Olivier Brunat verfasserin aut Perfect isometries and Murnaghan-Nakayama rules 2017 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier This article is concerned with perfect isometries between blocks of finite groups. Generalizing a method of Enguehard to show that any two p-blocks of (possibly different) symmetric groups with the same weight are perfectly isometric, we prove analogues of this result for p-blocks of alternating groups (where the blocks must also have the same sign when p is odd), of double covers of alternating and symmetric groups (for p odd, and where we obtain crossover isometries when the blocks have opposite signs), of complex reflection groups G(d,1,n) (for d prime to p), of Weyl groups of type B and D (for p odd), and of certain wreath products. In order to do this, we need to generalize the theory of blocks in a way which should be of independent interest. Nutzungsrecht: © Copyright 2017, American Mathematical Society Jean-Baptiste Gramain oth Enthalten in Transactions of the American Mathematical Society Providence, RI : American Mathematical Soc., 1900 369(2017), 11, Seite 7657 (DE-627)129501611 (DE-600)208386-3 (DE-576)014903210 0002-9947 nnns volume:369 year:2017 number:11 pages:7657 http://dx.doi.org/10.1090/tran/6860 Volltext http://www.ams.org/tran/2017-369-11/S0002-9947-2017-06860-4/ GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_24 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_120 GBV_ILN_130 GBV_ILN_2002 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2011 GBV_ILN_2015 GBV_ILN_2088 GBV_ILN_2409 GBV_ILN_4027 GBV_ILN_4036 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4266 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4310 GBV_ILN_4311 GBV_ILN_4314 GBV_ILN_4315 GBV_ILN_4317 GBV_ILN_4318 GBV_ILN_4323 GBV_ILN_4700 AR 369 2017 11 7657
spelling	10.1090/tran/6860 doi PQ20171228 (DE-627)OLC199715546X (DE-599)GBVOLC199715546X (PRQ)a654-1cb47f039bd09769251d316fd3c54b11a54ae20404239e3b68878c2a5d40fab00 (KEY)0042596620170000369001107657perfectisometriesandmurnaghannakayamarules DE-627 ger DE-627 rakwb eng 050 DE-101 510 AVZ Olivier Brunat verfasserin aut Perfect isometries and Murnaghan-Nakayama rules 2017 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier This article is concerned with perfect isometries between blocks of finite groups. Generalizing a method of Enguehard to show that any two p-blocks of (possibly different) symmetric groups with the same weight are perfectly isometric, we prove analogues of this result for p-blocks of alternating groups (where the blocks must also have the same sign when p is odd), of double covers of alternating and symmetric groups (for p odd, and where we obtain crossover isometries when the blocks have opposite signs), of complex reflection groups G(d,1,n) (for d prime to p), of Weyl groups of type B and D (for p odd), and of certain wreath products. In order to do this, we need to generalize the theory of blocks in a way which should be of independent interest. Nutzungsrecht: © Copyright 2017, American Mathematical Society Jean-Baptiste Gramain oth Enthalten in Transactions of the American Mathematical Society Providence, RI : American Mathematical Soc., 1900 369(2017), 11, Seite 7657 (DE-627)129501611 (DE-600)208386-3 (DE-576)014903210 0002-9947 nnns volume:369 year:2017 number:11 pages:7657 http://dx.doi.org/10.1090/tran/6860 Volltext http://www.ams.org/tran/2017-369-11/S0002-9947-2017-06860-4/ GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_24 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_120 GBV_ILN_130 GBV_ILN_2002 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2011 GBV_ILN_2015 GBV_ILN_2088 GBV_ILN_2409 GBV_ILN_4027 GBV_ILN_4036 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4266 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4310 GBV_ILN_4311 GBV_ILN_4314 GBV_ILN_4315 GBV_ILN_4317 GBV_ILN_4318 GBV_ILN_4323 GBV_ILN_4700 AR 369 2017 11 7657
allfields_unstemmed	10.1090/tran/6860 doi PQ20171228 (DE-627)OLC199715546X (DE-599)GBVOLC199715546X (PRQ)a654-1cb47f039bd09769251d316fd3c54b11a54ae20404239e3b68878c2a5d40fab00 (KEY)0042596620170000369001107657perfectisometriesandmurnaghannakayamarules DE-627 ger DE-627 rakwb eng 050 DE-101 510 AVZ Olivier Brunat verfasserin aut Perfect isometries and Murnaghan-Nakayama rules 2017 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier This article is concerned with perfect isometries between blocks of finite groups. Generalizing a method of Enguehard to show that any two p-blocks of (possibly different) symmetric groups with the same weight are perfectly isometric, we prove analogues of this result for p-blocks of alternating groups (where the blocks must also have the same sign when p is odd), of double covers of alternating and symmetric groups (for p odd, and where we obtain crossover isometries when the blocks have opposite signs), of complex reflection groups G(d,1,n) (for d prime to p), of Weyl groups of type B and D (for p odd), and of certain wreath products. In order to do this, we need to generalize the theory of blocks in a way which should be of independent interest. Nutzungsrecht: © Copyright 2017, American Mathematical Society Jean-Baptiste Gramain oth Enthalten in Transactions of the American Mathematical Society Providence, RI : American Mathematical Soc., 1900 369(2017), 11, Seite 7657 (DE-627)129501611 (DE-600)208386-3 (DE-576)014903210 0002-9947 nnns volume:369 year:2017 number:11 pages:7657 http://dx.doi.org/10.1090/tran/6860 Volltext http://www.ams.org/tran/2017-369-11/S0002-9947-2017-06860-4/ GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_24 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_120 GBV_ILN_130 GBV_ILN_2002 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2011 GBV_ILN_2015 GBV_ILN_2088 GBV_ILN_2409 GBV_ILN_4027 GBV_ILN_4036 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4266 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4310 GBV_ILN_4311 GBV_ILN_4314 GBV_ILN_4315 GBV_ILN_4317 GBV_ILN_4318 GBV_ILN_4323 GBV_ILN_4700 AR 369 2017 11 7657
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author	Olivier Brunat
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title_sort	perfect isometries and murnaghan-nakayama rules
title_auth	Perfect isometries and Murnaghan-Nakayama rules
abstract	This article is concerned with perfect isometries between blocks of finite groups. Generalizing a method of Enguehard to show that any two p-blocks of (possibly different) symmetric groups with the same weight are perfectly isometric, we prove analogues of this result for p-blocks of alternating groups (where the blocks must also have the same sign when p is odd), of double covers of alternating and symmetric groups (for p odd, and where we obtain crossover isometries when the blocks have opposite signs), of complex reflection groups G(d,1,n) (for d prime to p), of Weyl groups of type B and D (for p odd), and of certain wreath products. In order to do this, we need to generalize the theory of blocks in a way which should be of independent interest.
abstractGer	This article is concerned with perfect isometries between blocks of finite groups. Generalizing a method of Enguehard to show that any two p-blocks of (possibly different) symmetric groups with the same weight are perfectly isometric, we prove analogues of this result for p-blocks of alternating groups (where the blocks must also have the same sign when p is odd), of double covers of alternating and symmetric groups (for p odd, and where we obtain crossover isometries when the blocks have opposite signs), of complex reflection groups G(d,1,n) (for d prime to p), of Weyl groups of type B and D (for p odd), and of certain wreath products. In order to do this, we need to generalize the theory of blocks in a way which should be of independent interest.
abstract_unstemmed	This article is concerned with perfect isometries between blocks of finite groups. Generalizing a method of Enguehard to show that any two p-blocks of (possibly different) symmetric groups with the same weight are perfectly isometric, we prove analogues of this result for p-blocks of alternating groups (where the blocks must also have the same sign when p is odd), of double covers of alternating and symmetric groups (for p odd, and where we obtain crossover isometries when the blocks have opposite signs), of complex reflection groups G(d,1,n) (for d prime to p), of Weyl groups of type B and D (for p odd), and of certain wreath products. In order to do this, we need to generalize the theory of blocks in a way which should be of independent interest.
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title_short	Perfect isometries and Murnaghan-Nakayama rules
url	http://dx.doi.org/10.1090/tran/6860 http://www.ams.org/tran/2017-369-11/S0002-9947-2017-06860-4/
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