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Tilting Modules, Symmetric Functions, and the Module Structure of the Free Lie Algebra

✍ Scribed by Stephen Donkin; Karin Erdmann

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
302 KB
Volume
203
Category
Article
ISSN
0021-8693

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✦ Synopsis

Let E denote the natural module for the general linear group GL k n over an infinite field k of non-zero characteristic p. We consider here modules which are direct summands of the dth tensor power E md . The original motivation was to study the free Lie algebra. Let L be the d homogeneous component of degree d in the free Lie algebra L of rank n Ε½ . over k. Then GL k acts on L as the group of graded automorphisms in n such a way that L becomes the natural module E and more generally L 1 d

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