School of Mathematics

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Dr Alison E Parker

Associate Professor
Pure Mathematics

Contact details

Room: 8.28
Tel: +44 (0)113 3435126
Email: A.E.Parker @


Diagram algebras
Schur algebras
Representation theory
Algebraic groups

Research interests

The main area I am interested in is the modular representation theory of algebraic groups. This has connections with representation theory for the symmetric groups. In particular I am looking at homological properties of Schur algebras (S(n,r)) and quasi-hereditary algebras. I also look at diagram algebras and quasi-hereditary algebras. Recent results involve looking at growth rates for cohomology for algebraic groups.

Current postgraduate students

Amani Alfadhli (2014)
Eman Alluqmani (2014)
Ahmed Hussein (2012)


Parker AE, Stewart DI Stabilisation of the LHS spectral sequence for algebraic groups Journal of Lie Theory, 25, 807-813, 2015
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Parker AE, Stewart DI First cohomology groups for finite groups of Lie type in defining characteristic Bulletin of the London Mathematical Society, 46, 227-238, 2014
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Parker AE, Erdmann, K, Hannabuss, K.C. Bounding and unbounding higher extensions for SL2 Journal of Algebra, 389, 98-118, 2013
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Green RM, Martin PP, Parker AE A presentation for the symplectic blob algebra Journal of Algebra and its Applications, 11, 2012
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Parker A, Snashall N A family of Koszul self-injective algebras with finite Hochschild cohomology Journal of Pure and Applied Algebra, 216, 1245-1252, 2012
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Baur K, Erdmann K, Parker A Δ-filtered modules and nilpotent orbits of a parabolic subgroup in $\rm O_N$ Journal of Pure and Applied Algebra, 215, 885-901, 2011

Parker AE Higher extensions between modules for SL_2 Advances in Mathematics, 209, 381-405, 2007
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Martin P, Green RM, Parker A Towers of recollement and bases for diagram algebras: planar diagrams and a little beyond Journal of Algebra, 316, 392-452, 2007

Cox AG, Parker AE Homomorphisms between Weyl modules for SL_3(k). Transactions of the American Mathematical Society, 358, 4159-4207, 2006
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Parker AE Good $l$-filtrations for $q$-$\rm GL_3(k)$ Journal of Algebra, 304, 157-189, 2006

Cox A, Martin P, Parker A, Xi C Representation theory of towers of recollement: theory, notes, and examples Journal of Algebra, 302, 340-360, 2006

Cox A, Parker A Homomorphisms and higher extensions for Schur algebras and symmetric groups Journal of Algebra and its Applications, 4, 645-670, 2005

Mazorchuk V, Parker AE On the relation between finitistic and good filtration dimensions Communications in Algebra, 32, 1903-1916, 2004

Erdmann K, Parker AE On the global and $\nabla$-filtration dimensions of quasi-hereditary algebras Journal of Pure and Applied Algebra, 194, 95-111, 2004

Parker AE On the Weyl filtration dimension of the induced modules for a linear algebraic group Journal für die Reine und Angewandte Mathematik, 2003, 5-21
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Parker AE The Global Dimension of Schur Algebras for GL_2 and GL_3 Journal of Algebra, 241, 340-378, 2001
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