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University of Windsor

 






















Mathematics & Statistics
Lambton Tower, 10th Floor
Windsor, Ontario
Canada N9B 3P4
Tel: (519) 253-3000 Ext. 4711
Fax: (519) 971-3649

Office Hours:
Monday - Friday
8:30 am - 5:00 pm
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Dr. Francis W. Lemire
BSc (Windsor '64); MSc (Queens '65); PhD (Queens '67)
Professor
10-105 LT
Ext. 3030
Fax: (519) 971-3649
lemire@uwindsor.ca

Areas of Interest Lie Groups and Lie Algebras, Representation Theory

Research Outline The focus of my recent research is centered on the study of simple Lie Modules having finite dimensional weight space decompositions with respect to a fixed Cartan subalgebra.
Considerable progress has been made on the classification of such modules during the last few years. in particular, Olivier Mathieu has recently completed Fernando's classification scheme for all simple modules in this category by classifying all simple torsion free Lie modules of finite degree.Also in this direction D. Britten and I have established the Jordan Holder decompositions of tensor products of torsion free modules of degree one with finite dimensional simple modules. In particular we have shown that all simple torsion free Lie modules of finite degree can be realized as distinguished submodules of the tensor product of a torsion free module of degree one with an appropriate finite dimensional module. There are still a number of outstanding open problems in this area.
Selected Publications Britten,D.J., Lemire, F.W. 2001. Tensor Product Realizations of simple Torsion Free Modules, Canad. J. Math. Vol 53(2), 225-243.

Britten, D. J., Lemire, F. W., 1999. On Modules of Bounded Multiplicities For The Symplectic Algebra, Trans. AMS. Vol. 351(8), 3413-3431.

Britten, D. J., Lemire, F. W., 1998. The Torsion Free Pieri Formula, Can. J. Math. Vol. 50(2), 266-289.

Benkart, G. M., Britten, D. J., Lemire, F. W. 1997. Modules With Bounded Multiplicities For Simple Lie Algebras, Mathematische Zeitschrift,Vol. 225, 333-353.

Britten, D. J., Futorny, V. M., Lemire, F. W. 1995. Simple A2 Modules with a finite dimensional weight space. Communications in Alg. Vol.23(2), 467-510.

Britten, D.J., Lemire, F.W., 1994. On Level 0 Affine Lie Modules, Can, Math. Bull., Vol. 37, 310-314.

Lemire, F.W., 1994. Infinite Dimensional Lie Modules, Queen's Papers in Pure and Applied Mathemaics, Vol. 94, 67-72.

Britten, D. J., Hooper, J., Lemire, F. W. 1994. Simple Cn Modules with Multiplicities 1 and Applications, Can. J. Phys. Vol. 72(7&8), 326-335.

Britten, D. J., Lemire, F. W., Tarokh, V. A Constraint On The Existence of Simple Torsion Free Lie Modules, Proc. AMS, Vol. 123, (8), 1995.

Lemire, F. W. 1992. Torsion Free An-modules and Central Characters, Proceedings of the XIX International Colloquium, Group Theoretical Methods in Physics, Salamanca, Spain, Vol. I, 383-387.

Benkart, G., Britten, D. J., Lemire, F. W. 1992. Projection Maps for Tensor Products of gl(n,C) representations. Kyoto University Mathematics Journal, Vol. 28, (6), 983-1010.

Benkart, G., Britten, D. J., and Lemire, F. W. 1990. Stability in Modules for Classical Lie Algebras - A Constructive Approach, AMS in Their Memoirs Series, Vol. 85, 430, 165 pages.

Britten, D. J., Lemire, F. W., Zorzitto, F. 1990. Pointed Torsion Free Modules of Affine Lie Algebras, Com. in Alg., Vol. 18, 3307-3321.