G.D. James's Home Page

Professor G.D. James

Address:	Department of Mathematics Imperial College of Science, Technology and Medicine 180 Queen's Gate, London SW7 2AZ England
Office:	Room 675, Huxley Building
Tel:	+44 (0)20 7594 8499 (IC)
Fax:	+44 (0)20 7594 8517
E-mail:	g.james@imperial.ac.uk

Research Interests:

My research involves the representation theory of groups. I am particularly interested in symmetric groups and general linear groups and the combinatorics associated with them. A series of my papers has been concerned with evaluating decomposition numbers of various groups and establishing patterns in the decomposition matrices.
I also study q-analogues of the symmetric group algebra, especially Hecke algebras and q-Schur algebras. A collection of fundamental papers has established the relationship between repesentations of general linear groups in both the describing and non-describing characteristic cases and repesentations of symmetric groups. The main key in this area is the q-Schur algebra, which was introduced by R. Dipper and me.

Ph.D. Directions:

1. The study of decomposition matrices of symmetric groups.
2. The representation theory of Hecke algebras of various types.
3. The determinant is an example of a generalized matrix function. The relationship between such functions for certain classes of matrices involve many open problems.

Some Recent Publications:

G. James, Representations of general linear groups, in "Combinatorial and Geometric Representation Theory", ed. Seok-Jin Kang and Kyu-Hwan Lee, Contemporary Mathematics 325, Amer. Math. Soc. 2003, 93-107.
G. James and A. Mathas, Equating decomposition numbers for different primes, J. Algebra 258 (2002), 599-614.
G. James and A. Williams, Decomposition numbers of symmetric groups by induction, J. Algebra, 228 (2000), 119-142.
J. Graham and G. James, On a conjecture of Kleshchev and Gow concerning tensor products, J. Algebra 227 (2000), 767-782.
G. James and A. Mathas, The Jantzen sum formula for cyclotomic q-Schur algebras, Trans. Amer. Math. Soc., 352 (2000), 5381-5404.
G. James, Symmetric groups and related algebras, Textos de Matemática B, 19 (1999), 13-19.
G. James and A. Mathas, The irreducible Specht modules in characteristic 2, Bull. London Math. Soc., 31 (1999), 457-462.
G. James, Symmetric groups and Schur algebras, in "Algebraic Groups and their Representations", ed. R.W. Carter and J. Saxl, Kluwer Academic Press, 1998, 91-102.
R. Dipper, G. James and A. Mathas, The (Q,q)-Schur Algebra , Proc. London Math. Soc., 77 (1998), 327-361.
R. Dipper, G. James and A. Mathas, Cyclotomic q-Schur algebras, Math. Zeit., 229 (1998), 385-416.
G.D. James, C. Johnson and S. Pierce, Generalized matrix function inequalities on M-matrices, J. London Math. Soc., 57 (1998), 562-582.
R. Dipper, G. James and G.E. Murphy, Gram Determinants of Type B , J. Algebra, 189 (1997), 481-505.
G. James and A. Mathas, A q-analogue of the Jantzen-Schaper theorem, Proc. Lond. Math. Soc., 74 (1997), 241-274.
G. James and A. Mathas, Hecke algebras of type A at q=-1, J. Algebra, 184 (1996), 102-158.
J. Alperin and G.D. James, Bessel functions on finite groups, J. Algebra, 171(1995), 524-530.
R. Dipper, G. James and G.E. Murphy, Hecke algebras of type B at roots of unity, Proc. London Math. Soc., 70 (1995), 505-528.
G.D. James, Hecke algebras and immanants, Linear algebra and its applications, 197, 198 (1994), 659-670.
G.D. James, The representation theory of Buckminsterfullerene, J. Algebra, 167 (1994), 803-820.

Editorships:

Journal of Algebra

Linear and Multilinear Algebra

Prizes:

Smith's Prize 1970

Adam's Prize 1981-82 (aeq)

Research Grants:

Nato Grant for project "Representations of classical groups" 1987

SERC grant GR/J37690 for project "The modular representation theory of Coxeter groups and Hecke algebras", 1994.

EPSRC grant GR/K41571 for project "The representation theory of Hecke algebras", 1995.

EPSRC grant GR/N15931 for project "Representations of general linear groups ", 2000.

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