62 citations · 165 across the 21 of their papers we have counts for
21 papers
Whittaker modules for
Xiangqian Guo, Xuewen Liu, Limeng Xia
In this paper, we study the Whittaker modules for the quantum enveloping algebra $U_q(\sl_3)$ with respect to a fixed Whittaker function. We construct the universal Whittaker modul…
Smooth representations of affine Kac-Moody algebras
Vyacheslav Futorny, Xiangqian Guo, Yaohui Xue +1
Smooth modules for affine Kac-Moody algebras have a prime importance for the quantum field theory as they correspond to the representations of the universal affine vertex algebras.…
-Differential operators and -differential modules for the Virasoro algebra
Xuewen Liu, Li Guo, Xiangqian Guo
The concept of -differential operators is a natural generalization of differential operators and difference operators. In this paper, we determine the -differential Lie algeb…
$U(\fh)$-free modules over the Block algebra $\BB(q)$
Xuewen Liu, Xiangqian Guo
In this paper, we construct a new class of modules over the Block algebra $\BB(q)$, where is a nonzero complex number. We determined the irreducibilities of these modules and t…
Simple modules over the Lie algebras of divergence zero vector fields on a torus
Brendan Frisk Dubsky, Xianqian Guo, Yufeng Yao +1
Let be an integer, the Weyl algebra over the Laurent polynomial algebra , and the L…
Irreducible modules over the divergence zero algebras and their -analogues
Xuewen Liu, Xiangqian Guo, Zhen Wei
In this paper, we study a class of -graded modules, which are constructed using Larsson's functor from $\sl_d$-modules , for the Lie algebras of divergence zero vector fie…
New irreducible tensor product modules for the Virasoro algebra (II)
Xuewen Liu, Xiangqian Guo, Jing Wang
In this paper, we obtain a class of Virasoro modules by taking tensor products of the irreducible Virasoro modules and with irreducible highest weight modules…
New irreducible tensor product modules for the Virasoro algebra
Xiangqian Guo, Xuewen Liu, Jing Wang
In this paper, we obtain a class of Virasoro modules by taking tensor products of the irreducible Virasoro modules defined in \cite{CG}, with irreducible highest weight…
On the module structure of the center of hyperelliptic Krichever-Novikov algebras
Ben Cox, Mee Seong Im
We consider the coordinate ring of a hyperelliptic curve and let be the corresponding current Lie algebra where is a finite dimensional simple…
Simple Witt modules that are finitely generated over the cartan subalgebra
Xiangqian Guo, Genqiang Liu, Rencai Lu +1
Let be an integer, and be the Witt algebra and the weyl algebra over the Laurent polynomial algebra $A_d=\mathbb{C} [x_1^{\pm1}, x_2^{\pm1}, ..., x_d^…
Jet modules for the centerless Virasoro-like algebra
Xiangqian Guo, Genqiang Liu
In this paper, we studied the jet modules for the centerless Virasoro-like algebra which is the Lie algebra of the Lie group of the area-preserving diffeomorphisms of a -torus.…
Zero product determined Lie algebras
Matej Bresar, Xiangqian Guo, Genqiang Liu +2
A Lie algebra over a field is said to be zero product determined (zpd) if every bilinear map with the property that whenever…
Simple superelliptic Lie algebras
Ben Cox, Xiangqian Guo, Rencai Lu +1
Let , . Then we have the Riemann surfaces (commutative algebras) and The Lie algebras $\mathcal…
Modules over the Heisenberg-Virasoro and algebras
Hongjia Chen, Xiangqian Guo
In this paper, we consider the modules for the Heisenberg-Virasoro algebra and the W algebra . We determine the modules whose restriction to the Cartan subalgebra (modulo c…
-point Virasoro Algebras and Their Modules of Densities
Ben Cox, Xiangqian Guo, Rencai Lu +1
In this paper we introduce and study -point Virasoro algebras, $\tilde{\W_a}$, which are natural generalizations of the classical Virasoro algebra and have as quotients multipoi…
Irreducible representations of untwisted affine Kac-Moody algebras
Xiangqian Guo, Kaiming Zhao
In this paper we construct a class of new irreducible modules over untwisted affine Kac-Moody algebras , generalizing and including both highest weight mo…
Tensor product weight modules over the Virasoro algebra
Hongjia Chen, Xiangqian Guo, Kaiming Zhao
The tensor product of highest weight modules with intermediate series modules over the Virasoro algebra was discussed by Zhang [Z] in 1997. Since then the irreducibility problem fo…
The probability of rectangular unimodular matrices over $\F_q[x]$
Xiangqian Guo, Guangyu Yang
In this note, we compute the probability that a matrix can be extended to an invertible matrix over $\F_q[x]$, which turns out to be $(1-q^{k-n})(1-q^{k-1-n…
Harish-Chandra modules over the $\Q$ Heisenberg-Virasoro Algebra
Xiangqian Guo, Xuewen Liu, Kaiming Zhao
In this paper, it is proved that all irreducible Harish-Chandra modules over the $\Q$ Heisenberg-Virasoro algebra are of intermediate series (all weight spaces are 1-dimensional).
Classification of irreducible Harish-Chandra modules over the loop-Virasoro algebra
Xiangqian Guo, Rencai Lu, Kaiming Zhao
The loop-Virasoro algebra is the Lie algebra of the tensor product of the Virasoro algebra and the Laurent polynomial algebra. This paper classifies irreducible Harish-Chandra modu…
Classification of irreducible Harish-Chandra modules over generalized Virasoro algebras
Xiangqian Guo, Rencai Lu, Kaiming Zhao
Let be an arbitrary additive subgroup of and the corresponding generalized Virasoro algebra. In the present paper, irreducible weight modules with finite dimension…