# 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.

## 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

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