Professor G.D. James
||Department of Mathematics
Imperial College of Science, Technology and Medicine
180 Queen's Gate, London SW7 2AZ
||Room 675, Huxley Building
||+44 (0)20 7594 8499 (IC)
||+44 (0)20 7594 8517
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
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.
1. The study of decomposition matrices of symmetric groups.
2. The representation theory of Hecke algebras of various
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.,
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
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,
Algebra, 167 (1994), 803-820.
Journal of Algebra
Linear and Multilinear Algebra
Smith's Prize 1970
Adam's Prize 1981-82 (aeq)
Nato Grant for project "Representations of classical groups"
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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