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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Not for publication

Semigroups generated by projections
    (Define a projection semigroup to be a semigroup generated by linear projections that fix a subspace of codimenion 1. We classify finite projection semigroups in dimension 2 over the complex numbers.)
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A conjecture on simultaneous cores
    (This is a conjectured form for the number of (s,s+d,s+2d,...)-core partitions. You're welcome to try to prove it!)
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A note on Kostka numbers
    (This is a quick note on semistandard tableaux and the dominance order, following a discussion on MathOverflow.)
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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.)
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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).)
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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.)
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Regularising a partition on the abacus
    (We give (with proof) an algorithm for computing the e-regularisation of a partition just using abacus displays.)
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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.)
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Published

Defect 2 spin blocks of symmetric groups and canonical basis coefficients Represent. Theory 26 (2022), 134–178. pdf
Minimal partitions with a given s-core and t-core Ann. Comb., to appear. pdf
Crystals, regularisation and the Mullineux map J. Comb. Algebra, to appear. pdf
Irreducible projective representations of the alternating group which remain irreducible in characteristic 2 Adv. Math. 374 (2020), 107340. pdf
An interesting family of posets Disc. Math. 343 (2020), 111988. pdf
Simultaneous core multipartitions European J. Combin. 76 (2019) 138–158. pdf
Irreducible projective representations of the symmetric group which remain irreducible in characteristic 2 Proc. London Math. Soc. 116 (2018) 878–928. pdf
Dyck tilings and the homogeneous Garnir relations for graded Specht modules J. Algebraic Combin. 45 (2017) 1041–1082. pdf
(s,t)-cores: a weighted version of Armstrong's conjecture Electronic J. Combin. 23 (2016) #P4.32. pdf
Generalised column removal for graded homomorphisms between Specht modules (with Liron Speyer) J. Algebraic Combin. 44 (2016) 393–432. pdf
The irreducible representations of the alternating group which remain irreducible in characteristic p Trans. Amer. Math. Soc 368 (2016) 5807–5855. 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