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 @ leeds.ac.uk

Keywords

Diagram algebras
Schur algebras
Cohomology
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)

Publications

Parker AE, Stewart DI Stabilisation of the LHS spectral sequence for algebraic groups Journal of Lie Theory, 25, 807-813, 2015
View abstract

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
DOI:10.1112/blms/bdt087
View abstract

Parker AE, Erdmann, K, Hannabuss, K.C. Bounding and unbounding higher extensions for SL2 Journal of Algebra, 389, 98-118, 2013
DOI:10.1016/j.jalgebra.2013.02.044
View abstract

Green RM, Martin PP, Parker AE A presentation for the symplectic blob algebra Journal of Algebra and its Applications, 11, 2012
DOI:10.1142/S0219498812500600
View abstract

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
DOI:10.1016/j.jpaa.2011.12.011
View abstract

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
DOI:10.1016/j.jpaa.2010.06.032

Parker AE Higher extensions between modules for SL_2 Advances in Mathematics, 209, 381-405, 2007
DOI:10.1016/j.aim.2006.05.015
View abstract

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
DOI:10.1016/j.jalgebra.2007.04.013

Cox AG, Parker AE Homomorphisms between Weyl modules for SL_3(k). Transactions of the American Mathematical Society, 358, 4159-4207, 2006
DOI:10.1090/S0002-9947-06-03861-X
View abstract

Parker AE Good $l$-filtrations for $q$-$\rm GL_3(k)$ Journal of Algebra, 304, 157-189, 2006
DOI:10.1016/j.jalgebra.2006.04.020

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
DOI:10.1016/j.jalgebra.2006.01.009

Cox A, Parker A Homomorphisms and higher extensions for Schur algebras and symmetric groups Journal of Algebra and its Applications, 4, 645-670, 2005
DOI:10.1142/S0219498805001460

Mazorchuk V, Parker AE On the relation between finitistic and good filtration dimensions Communications in Algebra, 32, 1903-1916, 2004
DOI:10.1081/AGB-120029912

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
DOI:10.1016/j.jpaa.2004.04.005

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
DOI:10.1515/crll.2003.079
View abstract

Parker AE The Global Dimension of Schur Algebras for GL_2 and GL_3 Journal of Algebra, 241, 340-378, 2001
DOI:10.1006/jabr.2001.8759
View abstract