Abstract:

For the action of a real reductive group G on a real affine space W, the map from W to the spectrum of the ring of invariant polynomials is not always surjective. Therefore, we describe Luna's construction of a topological quotient of the  G-action on W. Following work of Richardson--Slodowy and Schwarz, we equip this topological quotient with a real semi-algebraic structure. If time permits, we look at one or two examples of such quotients and determine their semi-algebraic structures.

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