# Dr Anton Cox

## Contact

- Dr Anton Cox
- +44 (0)20 7040 0142
- a.g.cox@city.ac.uk

## Postal Address

Northampton Square

London

EC1V 0HB

United Kingdom

## About

### Overview

Dr Cox studied at Clare College, Cambridge (1990-4), and graduated with a BA(Hons) degree in Mathematics, followed by a Certificate of Advanced Study in Mathematics. He spent the next three years preparing his PhD at Queen Mary and Westfield College, University of London, graduating in 1997.

After working in Oxford, Stuttgart, and Bielefeld, he joined the Mathematics Department in 1999. He is currently Head of Department.

Dr Cox's research interests lie in representation theory, where he studies representations of algebraic groups and related algebraic objects. Recent collaborations have involved researchers in Australia and China, as well as at City and elsewhere in the UK.

Dr Cox is a member of the Representation Theory research group in the Centre for Mathematical Science.

### Qualifications

PhD Mathematics QMW, University of London, 1997

Cert of Adv Study in Mathematics, University of Cambridge, 1994

BA Mathematics, University of Cambridge, 1993

### Employment

2005 - 2008 City University London, Senior Lecturer

2001 - 2005 City University London, Lecturer

1999 - 2001 City University London, EPSRC PDRA

1998 - 1999 Bielefeld & Stuttgart Universities, EEC TMR research position

1997 - 1998 Oxford University, EPSRC PDRA

### Membership of professional bodies

2011 Institute of Mathematics & its Applications, Fellow

2001 London Mathematical Society, Member

## Research

### Research interests

- Representations of algebraic groups and related finite groups and algebras

- Representations of finite-dimensional algebras arising in algebraic statistical mechanics

## Publications

### Chapter

- Cox, A.G. (2016).
**Introduction to Representations of Algebras and Quivers.***Algebra, Logic and Combinatorics*World Scientific. ISBN 978-1-78634-032-0.

### Internet publication

- Bowman, C. and Cox, A.G.
**Modular decomposition numbers of cyclotomic Hecke and diagrammatic**

Cherednik algebras: A path theoretic approach.

### Journal articles (18)

- Bowman, C., Cox, A. and Speyer, L. (2017).
**A family of graded decomposition numbers for diagrammatic cherednik algebras.***International Mathematics Research Notices*,*2017*(9), pp. 2686–2734. doi:10.1093/imrn/rnw101. - Bowman, C. and Cox, A. (2014).
**Decomposition numbers for Brauer algebras of type G(m, p, n) in characteristic zero.***Journal of Pure and Applied Algebra*,*218*(6), pp. 992–1002. doi:10.1016/j.jpaa.2013.10.014. - Bowman, C., Cox, A.G. and De Visscher, M. (2013).
**Decomposition numbers for the cyclotomic Brauer algebras in characteristic zero.***Journal of Algebra*,*378*, pp. 103–132. doi:10.1016/j.jalgebra.2012.12.020. - Cox, A. and De Visscher, M. (2011).
**Diagrammatic Kazhdan-Lusztig theory for the (walled) Brauer algebra.***Journal of Algebra*,*340*(1), pp. 151–181. doi:10.1016/j.jalgebra.2011.05.024. - Cox, A., De Visscher, M. and Martin, P. (2011).
**Alcove geometry and a translation principle for the Brauer algebra.***Journal of Pure and Applied Algebra*,*215*(4), pp. 335–367. doi:10.1016/j.jpaa.2010.04.023. - Cox, A., De Visscher, M. and Martin, P. (2009).
**A geometric characterisation of the blocks of the Brauer algebra.***J LOND MATH SOC*,*80*, pp. 471–494. doi:10.1112/jlms/jdp039. - Cox, A., De Visscher, M. and Martin, P. (2009).
**The blocks of the Brauer algebra in characteristic zero.***Representation Theory*,*13*, pp. 272–308. doi:10.1090/S1088-4165-09-00305-7. - Cox, A., De Visscher, M., Doty, S. and Martin, P. (2008).
**On the blocks of the walled Brauer algebra.***J ALGEBRA*,*320*(1), pp. 169–212. doi:10.1016/j.jalgebra.2008.01.026. - Cox, A. (2007).
**The tilting tensor product theorem and decomposition numbers for symmetric groups.***ALGEBRAS AND REPRESENTATION THEORY*,*10*(4), pp. 307–314. doi:10.1007/s10468-007-9051-8. - Cox, A., Martin, P., Parker, A. and Xi, C. (2006).
**Representation theory of towers of recollement: Theory, notes, and examples.***J ALGEBRA*,*302*(1), pp. 340–360. doi:10.1016/j.jalgebra.2006.01.009. - Cox, A. and Parker, A. (2006).
**Homomorphisms between Weyl modules for SL3(k).***T AM MATH SOC*,*358*(9), pp. 4159–4207. - Cox, A. and Parker, A. (2005).
**Homomorphisms and Higher Extensions for Schur algebras and symmetric**

groups.*Journal of Algebra and its Applications*,*4*, pp. 645–670. doi:10.1142/S0219498805001460. - Cox, A., Graham, J. and Martin, P. (2003).
**The blob algebra in positive characteristic.***J ALGEBRA*,*266*(2), pp. 584–635. doi:10.1016/S0021-8693(03)00260-6. - Cox, A. (2001).
**Decomposition numbers for distant Weyl modules.***J ALGEBRA*,*243*(2), pp. 448–472. doi:10.1006/jabr.2001.8857. - Cox, A. and Erdmann, K. (2000).
**On Ext(2) between Weyl modules for quantum GL(n).***MATH PROC CAMBRIDGE*,*128*, pp. 441–463. - Cox, A. (2000).
**On the blocks of the infinitesimal Schur algebras.***Q J MATH*,*51*, pp. 39–56. - Cox, A. (1998).
**Ext(1) for Weyl modules for q-GL(2, k).***MATH PROC CAMBRIDGE*,*124*, pp. 231–251. - Cox, A. (1998).
**The blocks of the q-Schur algebra.***J ALGEBRA*,*207*(1), pp. 306–325.

## Education

### Undergraduate teaching

In 2013-14 Dr Cox is teaching

MA1603 Programming

MA2204 Mathematics for Economists Post-GCSE 3