Duality and Involutions Conference 2008
The conference "Duality and Involutions in Representation Theory" will be held at the National University of Ireland, Maynooth from August 19-22, 2008. The conference will focus on the representation theory of finite groups.
The usual contravariant-dual of a module is the module of linear functions on the underlying vector space. However, many other duality operations are considered in representation theory. Examples include the identification of projective and injective modules and the dualities of Schur-Weyl, Alvis-Curtis, Ringel, Lusztig and Poincare. Duality also makes its presence felt in such topics as the modular representation theory of the symmetric group, where the modules D^\lambda are quotients modulo the radical of a symmetric bilinear form.
One non-mathematical definition is that duality is the quality or condition of being two or twofold. So our topic includes the representation theory of groups in characteristic 2, special properties of conjugacy classes of involutions, the Frobenius-Schur indicator, the Schur index, spin modules of symmetric groups, quadratic forms, Clifford algebras and super algebras. We also consider the use of involutions to establish functional equations and identities in the theory of symmetric functions.
The conference topic should be interpreted loosely. We welcome participation from mathematicians working on `classical' Brauer block theory, the theory of algebras, character theory, structure of finite groups, representations of Lie groups, Hecke algebras, combinatorial representation theory, cohomology and invariant theory, integral representation theory and the theory of lattices and orders.
All lectures will take place in the John Hume Building, North Campus, NUI-Maynooth (JHL02 on the map).
- Dr. John Murray, NUI Maynooth
- Professor Rod Gow, University College Dublin
- Dr. Rachel Quinlan, NUI Galway