Abstract: A spline is an assignment of polynomials to vertices of a graph, where the difference of two polynomials along an edge must belong to an ideal that labels that edge. We consider a set of splines constructed from the group of signed permutations, whose edges and labels are defined using a type B or C Hessenberg space. This is the GKM construction for the equivariant cohomology of type B and C regular semisimple Hessenberg varieties H. These structures give rise to the (graded) dot action representations of the Weyl group of signed permutations. This talk will give a basis for and compute the first degree character of the dot action representation, entirely from the combinatorial data of H.
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