BassSerre theory for groupoids and CalogeroMoser spaces
Farkhod Eshmatov (Michigan)  Oberseminar Darstellungstheorie (DAS)
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When 
Oct 24, 2011 from 04:15 pm to 05:15 pm 
Where  Raum 1.016 (LipschitzSaal), MathematikZentrum, Endenicher Allee 60 
Contact Name  Sachinidis 
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Abstract: Let C_n be the nth CalogeroMoser space: the space of conjugacy classes of pairs of matrices (X,Y) in Mat_n(C) satisfying condition rk( XYYX+Id_n)=1. The group G of symplectic automorphisms of C[x,y] act transitively on C_n. Let G_n denotes the stabilizer of a point in C_n under G. In this talk, I will explain how to compute G_n using the BassSerre theory of groupoids. We associate to each action groupoid C_n x G an " orbifold" (graph of groups) consisting of orbits of certain subgroups of G. The group G_n can be identified with the fundamental group of this orbifold. Our computation are motivated by the fact that G_n are precisely the automorphism groups of (nonisomorphic) domains Morita equivalent to the first Weyl algebra. The problem of description of these automorphism groups was originally posed by T.Stafford. (This joint work with Y.Berest and A.Eshmatov.)