34 citations · 160 across the 31 of their papers we have counts for
22 papers · 1 filter
Bounding regularity of -modules
Wee Liang Gan, Khoa Ta
Let be a skeleton of the category of finite sets and injective maps, and the product of copies of . We prove that if an -module is generated in degree $\l…
Adjoint functors on the representation category of
Wee Liang Gan, Liping Li
In this paper we study adjunction relations between some natural functors on the representation category of the category of finite linearly ordered sets and order-preserving inject…
An inductive method for -modules
Wee Liang Gan, Liping Li
In this paper we introduce an inductive method to study -modules presented in finite degrees, where is a skeleton of the category of finitely totally ord…
Castelnuovo-Mumford regularity of representations of certain product categories
Wee Liang Gan, Liping Li
We show in this paper that representations of a finite product of categories satisfying certain combinatorial conditions have finite Castelnuovo-Mumford regularity if and only if t…
Linear stable range for homology of congruence subgroups via FI-modules
Wee Liang Gan, Liping Li
We answer positively a question of Church, Miller, Nagpal and Reinhold on existence of a linear bound on the presentation degree of the homology of a complex of FI-modules. This im…
An application of Nakayama functor in representation stability theory
Wee Liang Gan, Liping Li, Changchang Xi
Using the Nakayama functor, we construct an equivalence from a Serre quotient category of a category of finitely generated modules to a category of finite-dimensional modules. We t…
Bounds on homological invariants of VI-modules
Wee Liang Gan, Liping Li
We give bounds for various homological invariants (including Castelnuovo-Mumford regularity, degrees of local cohomology, and injective dimension) of finitely generated VI-modules…
Asymptotic behaviors of representations of graded categories with inductive functors
Wee Liang Gan, Liping Li
In this paper we describe an inductive machinery to investigate asymptotic behaviors of homology groups and related invariants of representations of certain graded combinatorial ca…
An inductive machinery for representations of categories with shift functors
Wee Liang Gan, Liping Li
We describe an inductive machinery to prove various properties of representations of a category equipped with a generic shift functor. Specifically, we show that if a property (P)…
Stable decompositions of certain representations of the finite general linear groups
Wee Liang Gan, John Watterlond
We prove that the irreducible decomposition of the permutation representation of GL(n,q) on GL(n,q)/GL(n-m,q) stabilizes for large n. We deduce, as a consequence, a representation…
A long exact sequence for homology of FI-modules
Wee Liang Gan
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-m…
A representation stability theorem for VI-modules
Wee Liang Gan, John Watterlond
A VI-module gives rise to a sequence of representations of the finite general linear groups. We prove that the sequence obtained from any finitely generated VI-module over an algeb…
On central stability
Wee Liang Gan, Liping Li
The notion of central stability was first formulated for sequences of representations of the symmetric groups by Putman. A categorical reformulation was subsequently given by Churc…
Coinduction functor in representation stability theory
Wee Liang Gan, Liping Li
We study the coinduction functor on the category of FI-modules and its variants. Using the coinduction functor, we give new and simpler proofs of (generalizations of) various resul…
Koszulity of directed categories in representation stability theory
Wee Liang Gan, Liping Li
In the first part of this paper, we study Koszul property of directed graded categories. In the second part of this paper, we prove a general criterion for an infinite directed cat…
Noetherian property of infinite EI categories
Wee Liang Gan, Liping Li
It is known that finitely generated FI-modules over a field of characteristic 0 are Noetherian. We generalize this result to the abstract setting of an infinite EI category satisfy…
Harish-Chandra homomorphisms and symplectic reflection algebras for wreath-products
Pavel Etingof, Wee Liang Gan, Victor Ginzburg +1
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 hamiltoni…
Reflection functors and symplectic reflection algebras for wreath products
Wee Liang Gan
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 ass…
Almost-commuting variety, D-modules, and Cherednik Algebras
Wee Liang Gan, Victor Ginzburg
We study a scheme M closely related to the set of pairs of n by n-matrices with rank 1 commutator. We show that M is a reduced complete intersection with n+1 irreducible components…
Chevalley restriction theorem for the cyclic quiver
Wee Liang Gan
We prove a Chevalley restriction theorem and its double analogue for the cyclic quiver.
Quantized symplectic oscillator algebras of rank one
Wee Liang Gan, Nicolas Guay, Apoorva Khare
A quantized symplectic oscillator algebra of rank 1 is a PBW deformation of the smash product of the quantum plane with U_q(sl_2). We study its representation theory, and in partic…
Quantization of Slodowy slices
Wee Liang Gan, Victor Ginzburg
We give a direct proof of (a slight generalization of) the recent result of A. Premet related to generalized Gelfand-Graev representations and of an equivalence due to Skryabin.