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 
Email: 
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 qanalogues of the symmetric group algebra, especially
Hecke algebras and qSchur algebras. A collection of fundamental
papers has established the relationship between repesentations of general
linear groups in both the describing and nondescribing characteristic
cases and repesentations of symmetric groups. The main key in this area
is the qSchur 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. SeokJin Kang and KyuHwan Lee, Contemporary Mathematics 325, Amer. Math. Soc. 2003, 93107.
 G. James and A. Mathas, Equating decomposition numbers for different primes, J. Algebra 258 (2002), 599614.

G. James and A. Williams, Decomposition numbers of symmetric groups
by induction, J. Algebra, 228 (2000), 119142.

J. Graham and G. James, On a conjecture of Kleshchev and Gow concerning
tensor products, J. Algebra 227 (2000), 767782.

G. James and A. Mathas, The Jantzen sum formula for cyclotomic qSchur
algebras, Trans. Amer. Math. Soc., 352 (2000), 53815404.

G. James, Symmetric groups and related algebras, Textos de Matemática
B, 19 (1999), 1319.

G. James and A. Mathas, The irreducible Specht modules in characteristic
2, Bull. London Math. Soc., 31 (1999), 457462.

G. James, Symmetric groups and Schur algebras, in "Algebraic
Groups and their Representations", ed. R.W. Carter and J. Saxl, Kluwer
Academic Press, 1998, 91102.

R. Dipper, G. James and A. Mathas, The (Q,q)Schur
Algebra , Proc. London Math. Soc., 77 (1998), 327361.

R. Dipper, G. James and A. Mathas, Cyclotomic qSchur algebras,
Math. Zeit., 229 (1998), 385416.

G.D. James, C. Johnson and S. Pierce, Generalized matrix function inequalities
on Mmatrices, J. London Math. Soc., 57 (1998), 562582.

R. Dipper, G. James and G.E. Murphy, Gram
Determinants of Type B , J. Algebra, 189 (1997), 481505.

G. James and A. Mathas, A
qanalogue of the JantzenSchaper theorem, Proc. Lond. Math. Soc.,
74
(1997), 241274.

G. James and A. Mathas, Hecke algebras of
type A at q=1, J. Algebra, 184 (1996), 102158.

J. Alperin and G.D. James, Bessel functions on finite
groups, J. Algebra, 171(1995), 524530.

R. Dipper, G. James and G.E. Murphy, Hecke algebras
of type B at roots of unity, Proc. London Math. Soc., 70
(1995),
505528.

G.D. James, Hecke algebras and immanants, Linear
algebra and its applications, 197, 198 (1994), 659670.

G.D. James, The representation theory of Buckminsterfullerene,
J.
Algebra, 167 (1994), 803820.
Editorships:
Journal of Algebra
Linear and Multilinear Algebra
Prizes:
Smith's Prize 1970
Adam's Prize 198182 (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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