# 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, University of London, United Kingdom, 1997
- Cert of Adv Study in Mathematics, University of Cambridge, United Kingdom, 1994
- BA Mathematics, University of Cambridge, United Kingdom, 1993

### Employment

- Senior Lecturer, City, University London, 2005 – 2008
- Lecturer, City, University London, 2001 – 2005
- EPSRC PDRA, City, University London, 1999 – 2001
- EEC TMR research position, Bielefeld & Stuttgart Universities, 1998 – 1999
- EPSRC PDRA, University of Oxford, 1997 – 1998

### Memberships of professional organisations

- Member, Institute of Mathematics, 2011 – present
- Member, London Mathematical Society, 2001 – present

## 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. (2016).
**Introduction to Representations of Algebras and Quivers.***Algebra, Logic and Combinatorics*(pp. 69–104). WORLD SCIENTIFIC (EUROPE). ISBN 978-1-78634-029-0.

### Journal articles (22)

- Barbier, S., Cox, A. and De Visscher, M. (2019).
**The blocks of the periplectic Brauer algebra in positive characteristic.***Journal of Algebra*,*534*, pp. 289–312. doi:10.1016/j.jalgebra.2019.06.016. - BOWMAN, C. and COX, A.G. (2018).
**MODULAR DECOMPOSITION NUMBERS OF CYCLOTOMIC HECKE AND DIAGRAMMATIC CHEREDNIK ALGEBRAS: A PATH THEORETIC APPROACH.***Forum of Mathematics, Sigma*,*6*. doi:10.1017/fms.2018.9. - 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. 80–102. 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. - Bowman, C., Cox, A. and Hazi, A.
**Path isomorphisms between quiver Hecke and diagrammatic Bott-Samelson**.

endomorphism algebras. - Bowman, C., Cox, A., Hazi, A. and Michailidis, D.
**Path combinatorics and light leaves for quiver Hecke algebras.**.

## Education

### Undergraduate teaching

In 2013-14 Dr Cox is teaching

MA1603 Programming

MA2204 Mathematics for Economists Post-GCSE 3