The n-dimensional matrix representations of a group or an associative algebra A form a space (algebraic variety) Rep(A,n) called the n-th representation variety of A. This is a classical geometric invariant that plays a role in many areas of mathematics. The construction of Rep(A,n) is natural (functorial) in A, but it is not `exactâ€™ in the sense of homological algebra. In this talk, we will explain how to refine Rep(A,n) by constructing a derived representation variety DRep(A,n), which is an example of a derived moduli space in algebraic geometry. For an application, we will look at the classical varieties of commuting matrices, and present a series of combinatorial conjectures extending the famous Macdonald conjectures in representation theory.

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- Seminars for 2016

Last updated: 17 Aug 2019