# School of Mathematics

## 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.

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