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|Title:||On the quiver and relations of the Borel Schur algebras|
|Presented at:||University of Leicester|
|Abstract:||Let K be an infinite field of characteristic p â‰¥ 0 and let n, r be positive integers. Let S+(n, r) be the Borel Schur algebra over K, which is a sub-algebra of the Schur algebra S(n, r). We aim to give a description of the Borel Schur algebra S+ (n, r) by finding its quiver and relations. We give a complete description of the quiver and relations for S+(2, r). We also construct a family of embedding from S+(2, r) to S+(n, r + s) which induce embeddings of the corresponding quivers. This gives us some relations for S+(n, r) for n > 2.;We describe the quiver of S+( n, r) for both p = 0 and p > 0. We also describe some relations of special type for p > 0 and find all relations for p = 0.|
|Rights:||Copyright © the author. All rights reserved.|
|Appears in Collections:||Theses, Dept. of Mathematics|
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