Pure Maths Colloquium: Problems in linear algebra related to root systems
1 December 2003 16:00 in CM221"Given matrices in known conjugacy classes, what can one say about the conjugacy class of their product? Equivalently, can one determine whether or not it is possible to solve the equation A1, A2...,Ak = I with matrices Ai belonging to prescribed conjugacy classes? A variant, the Deligne-Simpson problem, asks for the existence of irreducible solutions. These problems arise naturally in connection with the classification of differential equations on the Riemann sphere. I shall describe partial answers to these and analogous problems involving sums of matrices. The answers are in terms of root systems, as occurring for semisimple Lie algebras, or more generally for Kac-Moody Lie algebras. The proofs involve representations of quivers, vector bundles with parabolic structure and the Riemann-Hilbert correspondence."
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