Dr Matthew Fayers
Reader in Pure Mathematics
School of Mathematical Sciences
Queen Mary University of London
Queen Mary University of London
Research
Representation theory, Algebraic combinatorics, Finite groups, Hecke algebras, Quantum algebra
Interests
My research interests are in algebra and combinatorics, stemming mainly from the representation theory of the symmetric group in prime characteristic, and the associated combinatorics of integer partitions. Beyond the symmetric group, I study Iwahori-Hecke algebras and quantum Lie theory.Publications
Publications of specific relevance to the Centre for Combinatorics, Algebra and Number Theory2024
Fayers M, Kleshchev A and Morotti L (2024). Decomposition numbers for abelian defect RoCK blocks of double covers of symmetric groups. Journal of the London Mathematical Society, Wiley vol. 109 (2) 31-01-2024
2023
Fayers M (2023). Comparing Fock spaces in types $A^{(1)}$ and $A^{(2)}$. Algebraic Combinatorics, Cellule MathDoc/Centre Mersenne vol. 6 (5), 1347-1381. 07-11-2023
Fayers M and Morotti L (2023). On the irreducible spin representations of symmetric and alternating groups which remain irreducible in characteristic 3 3. Representation Theory of the American Mathematical Society, American Mathematical Society (AMS) vol. 27 (22), 778-814. 11-09-2023
2022
Fayers M (2022). Minimal Partitions with a Given s-Core and t-Core. Annals of Combinatorics, Springer, 1-32. 25-08-2022
Fayers M (2022). Crystals, regularisation and the Mullineux map. Journal of Combinatorial Algebra, European Mathematical Society - EMS - Publishing House vol. 6 (3), 315-352. 21-06-2022
Fayers M (2022). Defect 2 2 spin blocks of symmetric groups and canonical basis coefficients. Representation Theory of the American Mathematical Society, American Mathematical Society (AMS) vol. 26 (06), 134-178. 17-03-2022
2020
Fayers M (2020). Irreducible projective representations of the alternating group which remain irreducible in characteristic 2. Advances in Mathematics, Elsevier 05-08-2020
Fayers M (2020). 2-chains: an interesting family of posets. Discrete Mathematics, Elsevier 23-05-2020
2018
FAYERS M (2018). Simultaneous core multipartitions. European Journal of Combinatorics, Elsevier vol. 76 29-10-2018
2017
FAYERS M (2017). Irreducible projective representations of the symmetric group which remain irreducible in characteristic 2. Proceedings of the London Mathematical Society, London Mathematical Society 08-12-2017
2016
FAYERS M (2016). Dyck tilings and the homogeneous Garnir relations for graded Specht modules. Journal of Algebraic Combinatorics: an international journal, Springer Verlag (Germany) 27-12-2016
FAYERS M (2016). (s,t)-cores: a weighted version of Armstrong's conjecture. Electronic Journal of Combinatorics vol. 23 (4) 25-11-2016
Fayers M and Speyer L (2016). Generalised column removal for graded homomorphisms between Specht modules. Journal of Algebraic Combinatorics, Springer Nature vol. 44 (2), 393-432. 17-03-2016
2015
Fayers M (2015). THE IRREDUCIBLE REPRESENTATIONS OF THE ALTERNATING GROUP WHICH REMAIN IRREDUCIBLE IN CHARACTERISTIC p. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY vol. 368 (8), 5807-5855. 03-12-2015
2014
Fayers M (2014). A generalisation of core partitions. JOURNAL OF COMBINATORIAL THEORY SERIES A vol. 127, 58-84. 01-01-2014
2013
Fayers M and Lyle S (2013). The reducible Specht modules for the Hecke algebra HC,-1(On). JOURNAL OF ALGEBRAIC COMBINATORICS vol. 37 (2), 201-241. 01-01-2013
Barshevsky O, Fayers M and Schaps M (2013). A NON-RECURSIVE CRITERION FOR WEIGHTS OF A HIGHEST-WEIGHT MODULE FOR AN AFFINE LIE ALGEBRA. ISRAEL JOURNAL OF MATHEMATICS vol. 197 (1), 237-261. 01-01-2013
2012
Dodge CJ and Fayers M (2012). Some new decomposable Specht modules. JOURNAL OF ALGEBRA vol. 357, 235-262. 01-01-2012
Fayers M (2012). An algorithm for semistandardising homomorphisms. JOURNAL OF ALGEBRA vol. 364, 38-51. 01-01-2012
FAYERS M (2012). Irreducible Specht modules for Iwahori-Hecke algebras of type B. Represent. Theory vol. 16, 108-126. 01-01-2012
2011
2010
Fayers M (2010). An LLT-type algorithm for computing higher-level canonical bases. J PURE APPL ALGEBRA vol. 214 (12), 2186-2198. 01-12-2010
Fayers M (2010). Partition models for the crystal of the basic U-q((sl)over-cap(n))-module. J ALGEBR COMB vol. 32 (3), 339-370. 01-11-2010
Fayers M (2010). On the irreducible representations of the alternating group which remain irreducible in characteristic p p. Representation Theory of the American Mathematical Society, American Mathematical Society (AMS) vol. 14 (16), 601-626. 01-09-2010
Fayers M (2010). On the irreducible Specht modules for Iwahori-Hecke algebras of type A with q =-1. J ALGEBRA vol. 323 (6), 1839-1844. 15-03-2010
2009
Fayers M (2009). General runner removal and the Mullineux map. J ALGEBRA vol. 322 (12), 4331-4367. 15-12-2009
Fayers M and Lyle S (2009). Some reducible Specht modules for Iwahori-Hecke algebras of type A with q =-1. J ALGEBRA vol. 321 (3), 912-933. 01-02-2009
2008
Fayers M (2008). Weights of multipartitions and representations of Ariki-Koike algebras II: Canonical bases. J ALGEBRA vol. 319 (7), 2963-2978. 01-04-2008
Fayers M (2008). Decomposition numbers for weight three blocks of symmetric groups and Iwahori-Hecke algebras. T AM MATH SOC vol. 360 (3), 1341-1376. 01-01-2008
2007
Fayers M (2007). James's Conjecture holds for weight four blocks of Iwahori-Hecke algebras. J ALGEBRA vol. 317 (2), 593-633. 15-11-2007
Fayers M (2007). q-Analogues of regularisation theorems for linear and projective representations of the symmetric group. J ALGEBRA vol. 316 (1), 346-367. 01-10-2007
Fayers M (2007). Another runner removal theorem for v-decomposition numbers of Iwahori-Hecke algebras and q-Schur algebras. J ALGEBRA vol. 310 (1), 396-404. 01-04-2007
Fayers M and Tan KM (2007). The ordinary quiver of a weight three block of the symmetric group is bipartite. ADV MATH vol. 209 (1), 69-98. 15-02-2007
2006
Fayers M and Tan KM (2006). Adjustment matrices for weight three blocks of Iwahori-Hecke algebras. J ALGEBRA vol. 306 (1), 76-103. 01-12-2006
Fayers M, Lyle S and Martin S (2006). p-restriction of partitions and homomorphisms between Specht modules. J ALGEBRA vol. 306 (1), 175-190. 01-12-2006
Fayers M (2006). Weights of multipartitions and representations of Ariki-Koike algebras. ADV MATH vol. 206 (1), 112-144. 20-10-2006
Fayers M (2006). Weight two blocks of Iwahori-Hecke algebras of type B. J ALGEBRA vol. 303 (1), 154-201. 01-09-2006
2005
Fayers M (2005). Weight two blocks of Iwahori-Hecke algebras in characteristic two. MATH PROC CAMBRIDGE vol. 139, 385-397. 01-11-2005
Fayers M (2005). 0-Hecke algebras of finite Coxeter groups. J PURE APPL ALGEBRA vol. 199 (1-3), 27-41. 01-07-2005
Fayers M (2005). Irreducible Specht modules for Hecke algebras of type A. ADV MATH vol. 193 (2), 438-452. 01-06-2005
Fayers M (2005). Multiple-elimination knockout tournaments with the fixed-win property. DISCRETE MATH vol. 290 (1), 89-97. 28-01-2005
2004
Fayers M and Martin S (2004). Homomorphisms between Specht modules. MATH Z vol. 248 (2), 395-421. 01-10-2004
2003
Fayers M and Lyle S (2003). Row and column removal theorems for homomorphisms between Specht modules. J PURE APPL ALGEBRA vol. 185 (1-3), 147-164. 01-12-2003
Fayers M and Martin S (2003). General vertices in ordinary quivers for symmetric group algebras. J ALGEBRA vol. 263 (1), 88-118. 01-05-2003
2002
Fayers M (2002). On weight three blocks of symmetric groups in characteristic three. Q J MATH vol. 53, 403-419. 01-12-2002
Fayers M (2002). On the blocks of E-13 over a field of characteristic three. MATH PROC CAMBRIDGE vol. 133, 1-29. 01-07-2002
2001
Grants
Grants of specific relevance to the Centre for Combinatorics, Algebra and Number TheoryIrreducible modular representationsMatthew Fayers
£65,811 EPSRC Engineering and Physical Sciences Research Council (01-07-2022 - 31-12-2022)