A row removal theorem for the Ext quiver of symmetric groups and Schur algebras
Author:
David J. Hemmer
Journal:
Proc. Amer. Math. Soc. 133 (2005), 403414
MSC (2000):
Primary 20C30
Published electronically:
August 4, 2004
MathSciNet review:
2093061
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Abstract: In 1981, G. D. James proved two theorems about the decomposition matrices of Schur algebras involving the removal of the first row or column from a Young diagram. He established corresponding results for the symmetric group using the Schur functor. We apply James' techniques to prove that row removal induces an injection on the corresponding between simple modules for the Schur algebra. We then give a new proof of James' symmetric group result for partitions with the first part less than . This proof lets us demonstrate that firstrow removal induces an injection on Ext spaces between these simple modules for the symmetric group. We conjecture that our theorem holds for arbitrary partitions. This conjecture implies the KleshchevMartin conjecture that for any simple module in characteristic . The proof makes use of an interesting fixedpoint functor from modules to modules about which little seems to be known.
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Additional Information
David J. Hemmer
Affiliation:
Department of Mathematics, University of Toledo, 2801 W. Bancroft, Toledo, Ohio 43606
DOI:
http://dx.doi.org/10.1090/S0002993904075756
PII:
S 00029939(04)075756
Received by editor(s):
May 23, 2003
Received by editor(s) in revised form:
October 15, 2003
Published electronically:
August 4, 2004
Additional Notes:
The author’s research was supported in part by NSF grant DMS0102019
Communicated by:
Jonathan I. Hall
Article copyright:
© Copyright 2004 American Mathematical Society
