Algebra Seminar
Fall 2007
(Unless otherwise indicated, all talks are 11:30am-12:30pm at 9-118 Lambton Tower.)
1 October
Konstantina Christodoulopoulou (University of Windsor)
"Whittaker Modules I"
Abstract: I will give an introduction to Whittaker modules and discuss some basic examples.
15 October
Konstantina Christodoulopoulou (University of Windsor)
"Whittaker Modules II"
Abstract: I will describe the irreducible Whittaker modules for Heisenberg algebras and for the Lie algebra obtained by adjoining a degree derivation to an infinite-dimensional Heisenberg algebra. I will use these modules to construct a new class of irreducible modules for non-twisted affine Lie algebras.
22 October
No seminar
29 October
Konstantina Christodoulopoulou (University of Windsor)
"Whittaker Modules III: Imaginary Whittaker modules for affine Lie algebras"
Abstract: After a brief review, I will finish the construction of imaginary Whittaker modules and discuss some of their properties.
5 November: *This talk will be held in 256 Dillon Hall*
Tomas Pospichal (University of Windsor)
"Stratifications of Algebras and Categories"
Abstract: The study of highest weight modules in Lie theory inspired a number of notions of a "stratification" of an algebra or a category. An overview will be given, with an emphasis on associative algebras and module categories.
12 November
Wai Ling Yee (University of Windsor)
"The Dynkin-Kostant Classification of Nilpotent Orbits"
Abstract: While there are infinitely many semisimple orbits in a complex semisimple Lie algebra g, the number of nilpotent orbits is finite and bounded by 3^rank g. In sl_n, we can write down Jordan forms corresponding to each nilpotent orbit and establish a correspondence between partitions of n and nilpotent orbits. In the Dynkin-Kostant classification of nilpotent orbits, one finds a correspondence between nilpotent orbits and special copies of sl_2 in g, and then a correspondence between these special copies of sl_2 and certain semisimple orbits to which one attaches weighted Dynkin diagrams.
19 November
No seminar
26 November
Chris Brav (Queen's University)
"Relating McKay Correspondences"
Abstract: The original McKay correspondence associates an affine Dykin diagram to a finite subgroup G of SU(2) using the representation theory of G. There are two kinds of geometric realization of this correspondence, with G acting either on the projective line or on the affine plane. In the first case, the path algebra of the affine Dynkin quiver arises naturally out of the geometry; in the second, its preprojective algebra. I'll show how the cotangent bundle of the projective line provides a bridge between these two forms of the McKay correspondence.
3 December
Frank Lemire (University of Windsor)
"Simple highest weight modules with bounded multiplicities for affine Lie algebras"
Abstract: The goal is to outline the classification of the modules described in the title.
7 December
Frank Lemire (University of Windsor)
"Simple highest weight modules with bounded multiplicities for affine Lie algebras II"
Abstract: This talk will be a continuation of Monday's lecture on classification of bounded simple highest weight modules for affine Lie algebras.