arXiv subjects

C. Bowman

Publications and source records attributed to C. Bowman.

25 records · Page 2Linked to original sources

arXiv2014

Decomposition of Tensor Products of Modular Irreducible Representations for $SL_3$: the $p \geq 5$ case

We study the structure of the indecomposable direct summands of tensor products of two restricted simple $SL_3(K)$-modules, where $K$ is an algebraically closed field of characteristic $p \geq 5$. We give a characteristic-free algorithm for the computation of the decomposition of such a tensor product into indecomposable modules. The $p<5$ case for $\SL_3(K)$ was studied in the authors' earlier paper. In this paper we show that for characteristics $p\geq 5$ all the indecomposable summands are rigid, in contrast to the situation in characteristic 3.

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arXiv2013

Decomposition numbers for Brauer algebras of type G(m,p,n) in characteristic zero

We introduce Brauer algebras associated to complex reflection groups of type $G(m,p,n)$, and study their representation theory via Clifford theory. In particular, we determine the decomposition numbers of these algebras in characteristic zero.

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arXiv2012

A Reciprocity Result for Projective Indecomposable Modules of Cellular Algebras and BGG Algebras

We show that an adaptation of Landrock's Lemma for symmetric algebras also holds for cellular algebras and BGG algebras. This is a result relating the radical layers of any two projective modules. The reason it holds in our setting is that there is a duality between injective hulls and projective covers. As a corollary we deduce that BGG reciprocity respects Loewy structure.

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arXiv2012

Bases of quasi-hereditary covers of diagram algebras

We extend the the combinatorics of tableaux to the study of diagram algebras and give a uniform construction of their quasi-hereditary covers.

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arXiv2012

Decomposition numbers for the cyclotomic Brauer algebras in characteristic zero

We study the representation theory of the cyclotomic Brauer algebra via truncation to idempotent subalgebras which are isomorphic to a product of walled and classical Brauer algebras. In particular, we determine the block structure and decomposition numbers in characteristic zero.

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arXiv2011

Brauer algebras of Type $C$ are Cellularly Stratified Algebras

In a recent paper Cohen, Liu and Yu introduce the Type $C$ Brauer algebra. We show that this algebra is an iterated inflation of hyperoctahedral groups, and that it is cellularly stratified. This gives an indexing set of the standard modules, results on decomposition numbers, and the conditions under which the algebra is quasi-hereditary.

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arXiv2010

Decomposition of tensor products of modular irreducible representations for $SL_3$ (With an Appendix by C.M. Ringel)

We give an algorithm for working out the indecomposable direct summands in a Krull--Schmidt decomposition of a tensor product of two simple modules for G=SL_3 in characteristics 2 and 3. It is shown that there is a finite family of modules such that every such indecomposable summand is expressible as a twisted tensor product of members of that family. Along the way we obtain the submodule structure of various Weyl and tilting modules. Some of the tilting modules that turn up in characteristic 3 are not rigid; these seem to provide the first example of non-rigid tilting modules for algebraic groups. These non-rigid tilting modules lead to examples of non-rigid projective indecomposable modules for Schur algebras, as shown in the Appendix. Higher characteristics (for SL_3) will be considered in a later paper.

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