Some results on a variant of the Green correspondence with applications to Alperin's weight conjecture for blocks

2021 ◽  
Vol 15 (1) ◽  
pp. 37-47
Author(s):  
Morton E. Harris
Keyword(s):  
Green Correspondence

scholarly journals Green correspondence for virtually pro-p groups

2010 ◽  
Vol 323 (8) ◽  
pp. 2203-2208 ◽  
Author(s):  
J.W. MacQuarrie
Keyword(s):  
Green Correspondence

scholarly journals Indecomposable representations in characteristic two of the simple groups of order not divisible by eight

1976 ◽  
Vol 15 (3) ◽  
pp. 407-419 ◽  
Author(s):  
P.W. Donovan ◽  
M-R. Freislich
Keyword(s):  
Explicit Construction ◽  
Simple Groups ◽  
Indecomposable Representations ◽  
Characteristic Two ◽  
Green Correspondence

The indecomposable representations in characteristic two of the groups PSL(2, q) where q is congruent to 3 or 5 modulo 8 are classified. For q = 3 or 5 the classification is obtained by explicit construction of modules, using the Green correspondence to prove completeness. For larger q, the classification is obtained using equivalences between appropriate categories of modules.

A Remark on the Green Correspondence on G-Algebras

2005 ◽  
Vol 12 (04) ◽  
pp. 665-668 ◽  
Author(s):  
Morton E. Harris
Keyword(s):  
Finite Group ◽  
Green Correspondence

In the context of G-algebras, we prove that Green correspondent points satisfy some important properties that are suggested by the classical finite group Green correspondence.

scholarly journals Young modules for symmetric groups

2001 ◽  
Vol 71 (2) ◽  
pp. 201-210 ◽  
Author(s):  
Karin Erdmann
Keyword(s):  
Representation Theory ◽  
Finite Groups ◽  
Symmetric Groups ◽  
General Linear ◽  
Linear Groups ◽  
Schur Algebras ◽  
General Linear Groups ◽  
Green Correspondence

AbstractLet K be a field of characteristic p. The permutation modules associated to partitions of n, usually denoted as Mλ, play a central role not only for symmetric groups but also for general linear groups, via Schur algebras. The indecomposable direct summands of these Mλ were parametrized by James; they are now known as Young modules; and Klyachko and Grabmeier developed a ‘Green correspondence’ for Young modules. The original parametrization used Schur algebras; and James remarked that he did not know a proof using only the representation theory of symmetric groups. We will give such proof, and we will at the same time also prove the correspondence result, by using only the Brauer construction, which is valid for arbitrary finite groups.

scholarly journals Module covers and the Green correspondence

2015 ◽  
Vol 432 ◽  
pp. 62-71
Author(s):  
Tiberiu Coconeţ ◽  
Andrei Marcus
Keyword(s):  
Green Correspondence

Analogs of the Green and Puig correspondences for twisted group algebras

2016 ◽  
Vol 19 (1) ◽  
pp. 1-24
Author(s):  
Morton E. Harris
Keyword(s):  
Finite Group ◽  
Representation Theory ◽  
Finite Groups ◽  
Modular Representation ◽  
Group Algebras ◽  
Modular Representation Theory ◽  
Twisted Group ◽  
Standard Derivation ◽  
Green Correspondence

AbstractIn the modular representation theory of finite groups, we show that the standard derivation of the Green correspondence lifts to a derivation of a Green correspondence for twisted group algebras (Theorem 1.3). Then, from these results we derive a lift of the Puig correspondences for twisted group algebras (Theorem 1.6).Clearly twisted group algebras arise naturally in finite group modular representation theory. We conclude with some suggestions for applications in this mathematical area.

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