Abstract
Let be a prime number. We consider representations of - valenced Schurian schemes over a field of characteristic , especially the case that the cardinality of the underlying set can be divided by and not by . A typical example of such scheme is obtained by the following way. Let be a finite group of order , where is prime to , and let be a -subgroup of . Define the scheme by the action of on . In this case, we will show that the adjacency algebra is a direct sum of some Brauer tree algebras and simple algebras, and hence it has finite representation type.
Also we give some examples of the case that is the symmetric group of degree and is its Young subgroup.
Acknowledgement
The authors thank the referee for his/her careful reading of the article.
Citation
Akihide Hanaki. Yoshimasa Hieda. "Representations of -valenced Schurian schemes." SUT J. Math. 44 (2) 169 - 179, June 2008. https://doi.org/10.55937/sut/1234383502
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