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Dr. Daniel J. Britten


B.A., (Merrimack College), M.Sc., Ph.D. (Iowa)

Professor Emeritus

LT 10-105

Ext. 3024

Email: britten@uwindsor.ca

Area of Research

Lie Theory

Research Interests

My research interests are primarily in the classification and construction of simple infinite dimensional weight modules with finite dimensional weight spaces for simple Lie algebras over the complexes. Although the classification is complete in the case when the Lie algebra is finite dimensional, there are still open question on the explicit construction, on formulas for weight multiplicities, etc. Also we have begun to study the case when the simple Lie algebra is an affine algebra. We are classifying, "admissible modules for affine algebras", an analogue of Mathieu's admissible module for nontwisted affine algebras within in a category studied by Chari and Pressley.

Potential Research Projects for Graduate Students

·         Classify "admissible modules for affine algebras" in the nontwisted case

·         Once admissible module are classified, use this to construct coherent families following the lead of O. Mathieu.

·         Find multiplicity formulas for simple i dimensional weight modules with finite dimensional weight spaces when the simple algebra is finite dimensional.

·         Finish the work started by an M.Sc. on the explicit realization of simple torsion free An-modules with finite dimensional weight spaces.

Recent Publications

1.               Britten, D.J.; Lariviere, J.; Lemire, F.W., Tensor Products of Torsion Free Cn-modules of Finite Degree and Finite Dimensional Modules, Com. in Algebra, 2006, 34, 1-10

2.               Britten, D.J.; Khonmenko, O.; Lemire, F.W.; Mazorchuck, V., Complete Reducibility of Torsion Free Cn-Modules, J. of Alg., 2004, 276, 129-142

3.               Britten, D.J.; Lemire, F.W., Tensor Product Realization of Simple Torsion Free Modules, Can. J. Math., 2001, 53, 225-243.

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