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- Wee Liang Gan
- 2003

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 theory of PBW properties of quadratic algebras, to which this paper aims to be a modest contribution, originates from the pioneering work of Drinfeld (see [Dr1]). In particular, as we learned after publication of [EG] (to the embarrassment of two of us!), symplectic reflection algebras, as well as PBW theorems for them, were discovered by Drinfeld in… (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 hamiltonian 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)

- Wee Liang Gan
- 2008

We construct reflection functors on categories of modules over deformed wreath products of the preprojective algebra of a quiver. These functors give equivalences of categories associated to generic parameters which are in the same orbit under the Weyl group action. We give applications to the representation theory of symplectic reflection algebras of… (More)

- Wee Liang Gan
- 2009

We prove that the graph complex is a strong homotopy Lie (super) bialgebra.

- Steven V. Sam, David Speyer, +6 authors Liping Li
- 2016

This document was assembled by the organizers of the 2016 AIM workshop on representation stability (Andrew Putman, Steven Sam, David Speyer, Andrew Snowden) to serve as a guide to the literature in the subject. We thought this could be useful to newcomers to the area since, although the subject is still young, there is already a sizeable literature. For… (More)

- Wee Liang Gan, Liang Gan
- 2016

We construct a long exact sequence involving the homology of an FI-module. Using the long exact sequence, we give two methods to bound the Castelnuovo–Mumford regularity of an FI-module which is generated and related in finite degree. We also prove that for an FImodule which is generated and related in finite degree, if it has a nonzero higher homology,… (More)

- Xiaojun Chen, FARKHOD ESHMATOV, Wee Liang Gan
- 2009

Let M be a smooth, simply-connected, closed oriented manifold, and LM the free loop space of M . Using a Poincare duality model for M , we show that the reduced equivariant homology of LM has the structure of a Lie bialgebra, and we construct a Hopf algebra which quantizes the Lie bialgebra.

- Wee Liang Gan
- 2008

We prove that the graph complex is a strong homotopy Lie (super) bialgebra.

The theory of PBW properties of quadratic algebras, to which this paper aims to be a modest contribution, originates from the pioneering work of Drinfeld (see [Dr1]). In particular, as we learned after publication of [EG] (to the embarrassment of two of us!), symplectic reflection algebras and even more general reflection algebras considered in Section 3.6… (More)