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 |
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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.
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G. James and A. Williams, Decomposition numbers of symmetric groups
by induction, J. Algebra, 228 (2000), 119-142.
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J. Graham and G. James, On a conjecture of Kleshchev and Gow concerning
tensor products, J. Algebra 227 (2000), 767-782.
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G. James and A. Mathas, The Jantzen sum formula for cyclotomic q-Schur
algebras, Trans. Amer. Math. Soc., 352 (2000), 5381-5404.
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G. James, Symmetric groups and related algebras, Textos de Matemática
B, 19 (1999), 13-19.
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G. James and A. Mathas, The irreducible Specht modules in characteristic
2, Bull. London Math. Soc., 31 (1999), 457-462.
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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.
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R. Dipper, G. James and A. Mathas, The (Q,q)-Schur
Algebra , Proc. London Math. Soc., 77 (1998), 327-361.
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R. Dipper, G. James and A. Mathas, Cyclotomic q-Schur algebras,
Math. Zeit., 229 (1998), 385-416.
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G.D. James, C. Johnson and S. Pierce, Generalized matrix function inequalities
on M-matrices, J. London Math. Soc., 57 (1998), 562-582.
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R. Dipper, G. James and G.E. Murphy, Gram
Determinants of Type B , J. Algebra, 189 (1997), 481-505.
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G. James and A. Mathas, A
q-analogue of the Jantzen-Schaper theorem, Proc. Lond. Math. Soc.,
74
(1997), 241-274.
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G. James and A. Mathas, Hecke algebras of
type A at q=-1, J. Algebra, 184 (1996), 102-158.
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J. Alperin and G.D. James, Bessel functions on finite
groups, J. Algebra, 171(1995), 524-530.
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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.
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G.D. James, Hecke algebras and immanants, Linear
algebra and its applications, 197, 198 (1994), 659-670.
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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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