A class of Schur algebras
Author:
M. Brender
Journal:
Trans. Amer. Math. Soc. 248 (1979), 435444
MSC:
Primary 20C05
MathSciNet review:
522268
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Abstract: This paper delineates a class of Schur algebras over a finite group G, parametrized by two subgroups . The constructed Schur algebra is maximal for the two properties (a) centralizing the elements of H, and (b) containing the elements of K in the identity. Most commonly considered examples of Schur algebras fall into this class. A complete set of characters of is given in terms of the spherical functions on the group G with respect to the subgroup H. Necessary and sufficient conditions are given for this Schur algebra to be commutative, in terms of a condition on restriction multiplicities of characters. This leads to a secondorthogonalitytype relation among a subset of the spherical functions. Finally, as an application, a particular Schur algebra of this class is analyzed, and shown to be a direct sum of centralizer rings.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947197905222687
PII:
S 00029947(1979)05222687
Keywords:
Schur algebra,
Sring,
semisimple algebra,
finite group,
spherical function,
character,
double coset algebra,
centralizer ring
Article copyright:
© Copyright 1979
American Mathematical Society
