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A basic set for the alternating group
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Published/Copyright:
January 20, 2010
Abstract
This article is concerned with the p-basic set existence problem in the representation theory of finite groups. We show that, for any odd prime p, the alternating group 𝔄n has a p-basic set. More precisely, we prove that the symmetric group 𝔖n has a p-basic set with some additional properties, allowing us to deduce a p-basic set for 𝔄n. Our main tool is the concept of generalized perfect isometries introduced by Külshammer, Olsson and Robinson. As a consequence we obtain some results on the decomposition numbers of 𝔄n.
Received: 2008-11-18
Revised: 2009-01-20
Published Online: 2010-01-20
Published in Print: 2010-April
© Walter de Gruyter Berlin · New York 2010
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Articles in the same Issue
- The Dirac operator on compact quantum groups
- Pair correlation of sums of rationals with bounded height
- Existence and uniqueness of constant mean curvature foliation of asymptotically hyperbolic 3-manifolds II
- Crossed products by minimal homeomorphisms
- On the facial structure of the unit ball in a JB*-triple
- Adjoint ideals along closed subvarieties of higher codimension
- On surfaces of general type with maximal Albanese dimension
- A basic set for the alternating group
- The twisted fourth moment of the Riemann zeta function
