# Matthew Fayers – papers

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For published papers, the versions linked at the right-hand side are my own. Links to the published versions are provided to comply with copyright requirements. If you enjoy journal typesetting and you have a journal subscription (or are very rich), then you might want to try these.

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## Submitted

 An interesting family of posets pdf Defect 2 spin blocks of symmetric groups and canonical basis coefficients pdf

## Not for publication

 A note on Kostka numbers (This is a quick note on semistandard tableaux and the dominance order, following a discussion on MathOverflow.) pdf Data for weight 2 blocks of Hecke algebras of type A (This summarises data on decomposition numbers and extensions between simple modules for weight two blocks of Hecke algebras. In a sense nothing is new here, only the way it is presented, which gives easy descriptions of the composition lengths of Specht modules and indecomposable projectives. In principle one could do the same thing for weight 3 (at least for decomposition numbers), but in practice this might be rather a lot of work.) pdf The $$n$$-bar-core of an $$m$$-bar-core (This is an analogue of the paper 'The $$t$$-core of an $$s$$-core' below. We consider bar-cores instead of cores, and prove essentially the same results (though there is slightly less symmetry in this case).) pdf Classifying level 1 Fock spaces of a certain type (This note arose from a discussion with Peter Tingley. We consider the possibility of defining a new version of the level 1 Fock space in type $$A^{(1)}$$ in which the transition coefficients between partitions are all powers of $$q$$. We show that in fact it's not possible to find anything new under this restriction. This note is very informal and sketchy.) pdf Regularising a partition on the abacus (We give (with proof) an algorithm for computing the e-regularisation of a partition just using abacus displays.) pdf Core blocks of Ariki–Koike algebras II: the weight of a core block (This is on the combinatorics of multipartitions and Ariki–Koike algebras. I submitted this paper for publication, but a very helpful referee showed that if you translate into the language of highest-weight representations for Kac–Moody algebras, then a large part of the paper is just finding the non-zero weight spaces for an irreducible highest-weight module, which is done in Kac's book. So this is not really publishable, but the results may be useful to somebody in this form.) pdf

## Published

 Simultaneous core multipartitions pdf Irreducible projective representations of the symmetric group which remain irreducible in characteristic 2 pdf Dyck tilings and the homogeneous Garnir relations for graded Specht modules pdf (s,t)-cores: a weighted version of Armstrong's conjecture pdf Generalised column removal for graded homomorphisms between Specht modules (with Liron Speyer) pdf The irreducible representations of the alternating group which remain irreducible in characteristic p pdf A generalisation of core partitions pdf A non-recursive criterion for weights of a highest weight module for an affine Lie algebra (with Orly Barshevsky and Malka Schaps) pdf An algorithm for semistandardising homomorphisms pdf The reducible Specht modules for the Hecke algebra $$\mathcal H_{\mathbb C,\!{-}\!1}(\mathfrak S_n)$$ (with Sinéad Lyle) pdf Some new decomposable Specht modules (with Craig Dodge) (note: this is a non-trivial update of the published version) pdf Irreducible Specht modules for Iwahori–Hecke algebras of type $$B$$ pdf The $$t$$-core of an $$s$$-core pdf On the irreducible representations of the alternating group which remain irreducible in characteristic $$p$$ pdf An LLT-type algorithm for computing higher-level canonical bases pdf Partition models for the crystal of the basic $$U_q(\widehat{\mathfrak{sl}}_n)$$-module pdf On the irreducible Specht modules for Iwahori–Hecke algebras of type $$A$$ with $$q={-}\!1$$ pdf Regularisation and the Mullineux map pdf Some reducible Specht modules for Iwahori–Hecke algebras of type $$A$$ with $$q={-}\!1$$ (with Sinéad Lyle) pdf General runner removal and the Mullineux map J. Algebra 322 (2009) 4331–4367. pdf Weights of multipartitions and representations of Ariki–Koike algebras II: canonical bases pdf James's Conjecture holds for weight four blocks of Iwahori–Hecke algebras pdf An extension of James's Conjecture pdf $$q$$-analogues of regularisation theorems for linear and projective representations of the symmetric group pdf Another runner removal theorem for $$v$$-decomposition numbers of Iwahori–Hecke algebras and $$q$$-Schur algebras pdf Core blocks of Ariki–Koike algebras pdf The ordinary quiver of a weight three block of the symmetric group is bipartite (with Kai Meng Tan) pdf Adjustment matrices for weight three blocks of Iwahori–Hecke algebras (with Kai Meng Tan) pdf $$p$$-restriction of partitions and homomorphisms between Specht modules (with Sinéad Lyle and Stuart Martin) pdf Weight two blocks of Iwahori–Hecke algebras of type $$B$$ pdf Decomposition numbers for weight three blocks of symmetric groups and Iwahori–Hecke algebras pdf Weights of multipartitions and representations of Ariki–Koike algebras (note: this is a non-trivial update of the published version) pdf Weight two blocks of Iwahori–Hecke algebras in characteristic two pdf 0-Hecke algebras of finite Coxeter groups pdf Irreducible Specht modules for Hecke algebras of type $$A$$ pdf A theorem concerning homomorphisms between Specht modules J. Algebra, to appear. pdf Homomorphisms between Specht modules (with Stuart Martin) pdf $$q$$-Schur subalgebras pdf Reducible Specht modules pdf Row and column removal theorems for homomorphisms between Specht modules (with Sinéad Lyle) pdf General vertices in ordinary quivers of symmetric group algebras (with Stuart Martin) pdf On the structure of Specht modules pdf On weight three blocks of symmetric groups in characteristic three pdf Schur subalgebras II pdf Schur subalgebras (with Stuart Martin) pdf On the blocks of $$\mathfrak S_{13}$$ over a field of characteristic three pdf

## Recreational papers

 Multiple-elimination knockout tournaments with the fixed-win property Disc. Math. 290 (2005) 89–97. pdf