Wee Liang Gan

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We introduce the notion of a dioperad to describe certain operations with multiple inputs and multiple outputs. The framework of Koszul duality for operads is generalized to dioperads. We show that the Lie bialgebra dioperad is Koszul. The current interests in the understanding of various algebraic structures using operads is partly due to the theory of(More)
The main result of the paper is a natural construction of the spherical subalgebra in a symplectic reflection algebra associated with a wreath-product in terms of quantum hamilto-nian reduction of an algebra of differential operators on a representation space of an extended Dynkin quiver. The existence of such a construction has been conjectured in [EG]. We(More)
We prove a Chevalley restriction theorem and its double analogue for the cyclic quiver. The aim of this paper is to prove a Chevalley restriction theorem and its double analogue for the cyclic quiver. When the quiver is of type A 0 , we recover the results for gl n. The proof of our Chevalley restriction theorem is similar to the proof for gl n ; however,(More)