# 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

 Simultaneous core multipartitions pdf Irreducible projective representations of the symmetric group which remain irreducible in characteristic 2 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## Not for publication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

 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 J. Combin. Theory Ser. A 127 (2014) 58–84. pdf A non-recursive criterion for weights of a highest weight module for an affine Lie algebra (with Orly Barshevsky and Malka Schaps) Israel J. Math. 197 (2013) 237–261. pdf An algorithm for semistandardising homomorphisms J. Algebra 364 (2012) 38–51. pdf The reducible Specht modules for the Hecke algebra $$\mathcal H_{\mathbb C,\!{-}\!1}(\mathfrak S_n)$$ (with Sinéad Lyle) J. Algebraic Combin. 37 (2013) 201–241. pdf Some new decomposable Specht modules (with Craig Dodge) (note: this is a non-trivial update of the published version) J. Algebra 357 (2012) 235–262. pdf Irreducible Specht modules for Iwahori–Hecke algebras of type $$B$$ Represent. Theory 16 (2012) 108–126. pdf The $$t$$-core of an $$s$$-core J. Combin. Theory Ser. A 118 (2011) 1525–1539. pdf On the irreducible representations of the alternating group which remain irreducible in characteristic $$p$$ Represent. Theory 14 (2010) 601–626. pdf An LLT-type algorithm for computing higher-level canonical bases J. Pure Appl. Algebra 214 (2010) 2186–2198. pdf Partition models for the crystal of the basic $$U_q(\widehat{\mathfrak{sl}}_n)$$-module J. Algebraic Combin. 32 (2010) 339–370. pdf On the irreducible Specht modules for Iwahori–Hecke algebras of type $$A$$ with $$q={-}\!1$$ J. Algebra 323 (2010) 1839–1844. pdf Regularisation and the Mullineux map Electronic J. Combin. 15 (2008) #R142. pdf Some reducible Specht modules for Iwahori–Hecke algebras of type $$A$$ with $$q={-}\!1$$ (with Sinéad Lyle) J. Algebra 321 (2009) 912–933. 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 J. Algebra 319 (2008) 2963–2978. pdf James's Conjecture holds for weight four blocks of Iwahori–Hecke algebras J. Algebra 317 (2007) 593–633. pdf An extension of James's Conjecture Int. Math. Res. Notices 2007 no. 10 Art. ID rnm032. pdf $$q$$-analogues of regularisation theorems for linear and projective representations of the symmetric group J. Algebra 316 (2007) 346–367. pdf Another runner removal theorem for $$v$$-decomposition numbers of Iwahori–Hecke algebras and $$q$$-Schur algebras J. Algebra 310 (2007) 396–404. pdf Core blocks of Ariki–Koike algebras J. Algebraic Combin. 26 (2007) 47–81. pdf The ordinary quiver of a weight three block of the symmetric group is bipartite (with Kai Meng Tan) Adv. Math. 209 (2007) 69–98. pdf Adjustment matrices for weight three blocks of Iwahori–Hecke algebras (with Kai Meng Tan) J. Algebra 306 (2006) 76–103. pdf $$p$$-restriction of partitions and homomorphisms between Specht modules (with Sinéad Lyle and Stuart Martin) J. Algebra 306 (2006) 175–190. pdf Weight two blocks of Iwahori–Hecke algebras of type $$B$$ J. Algebra 301 (2006) 154–201. pdf Decomposition numbers for weight three blocks of symmetric groups and Iwahori–Hecke algebras Trans. Amer. Math. Soc. 360 (2008) 1341–1376. pdf Weights of multipartitions and representations of Ariki–Koike algebras (note: this is a non-trivial update of the published version) Adv. Math. 206 (2006) 112–144. pdf Weight two blocks of Iwahori–Hecke algebras in characteristic two Math. Proc. Cambridge Philos. Soc. 139 (2005) 385–397. pdf 0-Hecke algebras of finite Coxeter groups J. Pure Appl. Algebra 199 (2005) 27–41. pdf Irreducible Specht modules for Hecke algebras of type $$A$$ Adv. Math. 193 (2005) 438–452. pdf A theorem concerning homomorphisms between Specht modules J. Algebra, to appear. pdf Homomorphisms between Specht modules (with Stuart Martin) Math. Z. 248 (2004) 395–421. pdf $$q$$-Schur subalgebras Algebr. Represent. Theory 8 (2005) 415–426. pdf Reducible Specht modules J. Algebra 280 (2004) 500–504. pdf Row and column removal theorems for homomorphisms between Specht modules (with Sinéad Lyle) J. Pure Appl. Algebra 185 (2003) 147–164. pdf General vertices in ordinary quivers of symmetric group algebras (with Stuart Martin) J. Algebra 263 (2003) 88–118. pdf On the structure of Specht modules J. London Math. Soc. 67 (2003) 85–102. pdf On weight three blocks of symmetric groups in characteristic three Quart. J. Math. 53 (2002) 403–419. pdf Schur subalgebras II J. Algebra 252 (2002) 300–321. pdf Schur subalgebras (with Stuart Martin) J. Algebra 240 (2001) 859–873. pdf On the blocks of $$\mathfrak S_{13}$$ over a field of characteristic three Math. Proc. Cambridge Philos. Soc. 133 (2002) 1–30. pdf

## Recreational papers

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