The Saito determinant for Coxeter discriminant strata
Misha Feigin (University of Glasgow)
Monday 12th October, 2020 16:00-17:00 Online
The orbit space V/W in the reflection representation V of a finite Coxeter group W carries a remarkable Saito metric which is flat. It can be defined as a Lie derivative of the invariant bilinear form on V. It forms a key part of the Frobenius manifold structure on the orbit space V/W. We are interested in the restriction of the Saito metric and of other Frobenius manifolds structures to the discriminant strata. We find determinant of the restricted Saito metric, which appears to have a factorised form. This determinant may be thought of as a generalisation of the Jacobian of the Coxeter group W for discriminant strata. The talk is based on the joint work with Georgios Antoniou and Ian Strachan.
The talk will be preceded by a 30 minute tea time. The Zoom link for the seminar is https://uofglasgow.zoom.us/j/91412568415 and the passcode is the genus of the two-dimensional sphere (4 letters).
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