Schur Subalgebras

Young Modules and Schur Subalgebras

Let K r be the group algebra of the symmetric group on r symbols over a eld K of prime characteristic p. This work is motivated by the problem of comparing modules in blocks of K r of a xed core and for varying weight w, where r 2 N is arbitrary. We approach this via polynomial representations of the general linear groups GL n (K) or equivalently via Schur algebras. The main part of the thesis ...

Schur Subalgebras and an Application to the Symmetric Group

Multiplicity Free Schur, Skew Schur, and Quasisymmetric Schur Functions

In this paper we classify all Schur functions and skew Schur functions that are multiplicity free when expanded in the basis of fundamental quasisymmetric functions, termed F -multiplicity free. Combinatorially, this is equivalent to classifying all skew shapes whose standard Young tableaux have distinct descent sets. We then generalize our setting, and classify all F -multiplicity free quasisy...

Covariant Presheaves and Subalgebras

For small involutive and integral quantaloids Q it is shown that covariant presheaves on symmetric Q-categories are equivalent to certain subalgebras of a speci c monad on the category of symmetric Q-categories. This construction is related to a weakening of the subobject classi er axiom which does not require the classi cation of all subalgebras, but only guarantees that classi able subalgebra...

Low n Boolean Subalgebras

Every lown Boolean algebra, for 1 ≤ n ≤ 4, is isomorphic to a computable Boolean algebra. It is not yet known whether the same is true for n > 4. However, it is known that there exists a low5 subalgebra of the computable atomless Boolean algebra which, when viewed as a relation on the computable atomless Boolean algebra, does not have a computable copy. We adapt the proof of this recent result ...