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Ext spaces for general linear and symmetric groups

Published online by Cambridge University Press:  14 November 2011

Stuart Martin
Affiliation:
Magdalene College, Cambridge CB3 OAG, England, U.K.

Synopsis

We consider the links between Ext1 groups of simple modules for the symmetric group, and Ext1 of simple modules for the general linear group.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 1991

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References

1Carter, R. W. and Lusztig, G.. On the modular representation theory of the general linear and symmetric groups. Math. Z. 136 (1974), 193242.CrossRefGoogle Scholar
2Donkin, S.. A note on decomposition numbers for reductive algebraic groups. J. Algebra 80 (1983), 226234.CrossRefGoogle Scholar
3Donkin, S.. A note on decomposition numbers for general linear and symmetric groups. Math. Proc. Cambridge Philos. Soc. 97 (1985), 5762.CrossRefGoogle Scholar
4Donkin, S.. Rational representations of algebraic groups, Lecture Notes in Mathematics, 1140 (Berlin: Springer, 1985).CrossRefGoogle Scholar
5Donkin, S.. On Schur algebras and related algebras I. J. Algebra 104 (1986), 310328.CrossRefGoogle Scholar
6Donkin, S.. On Schur algebras and related algebras II. J. Algebra 111 (1987), 354364.CrossRefGoogle Scholar
7Erdmann, K.. Schur algebras of finite type, (submitted to Quart. J. Math.)Google Scholar
8Fettes, S.. A theorem on Ext1 for the symmetric group. Comm. Algebra 13(6) (1985), 12991304.CrossRefGoogle Scholar
9Green, J. A.. Polynomial representations of GL n, Lecture Notes in Mathematics, 830 (Berlin: Springer, 1980).Google Scholar
10James, G. D.. On the decomposition numbers of the symmetric groups III. J. Algebra 71 (1981), 115122.CrossRefGoogle Scholar
11James, G. D.. Trivial source modules for symmetric groups. Archiv. Math. (Basel) 41 (1983), 294300.CrossRefGoogle Scholar
12James, G. D. and Kerber, A.. The representation theory of the symmetric groups, Encyclop. Math. 16 (Reading, Mass.: Addison-Wesley, 1981).Google Scholar
13Martin, S.. On the ordinary quiver of the principal block of certain symmetric groups. Quart. J. Math. Oxford Ser. (2) 40 (1989), 209223.CrossRefGoogle Scholar
14Martin, S.. Projective indecomposable modules for symmetric groups I. (submitted to Quart J. Math.)Google Scholar
15Scopes, J. C.. Representations of the symmetric groups (D. Phil. Thesis, University of Oxford, 1990).Google Scholar