scholarly journals A lower bound for the dimension of a highest weight module

2017 ◽  
Vol 21 (20) ◽  
pp. 611-625 ◽  
Author(s):  
Daniel Goldstein ◽  
Robert Guralnick ◽  
Richard Stong
Keyword(s):  
Lower Bound ◽  
Weight Module ◽  
Highest Weight Module ◽  
Highest Weight

A Family of Non-weight Modules over the Virasoro Algebra

2020 ◽  
Vol 27 (04) ◽  
pp. 807-820
Author(s):  
Guobo Chen
Keyword(s):  
Tensor Product ◽  
Sufficient Conditions ◽  
Virasoro Algebra ◽  
Necessary And Sufficient Conditions ◽  
Weight Module ◽  
Highest Weight Module ◽  
Isomorphism Classes ◽  
Highest Weight ◽  
Necessary And Sufficient ◽  
Weight Modules

In this paper, we consider the tensor product modules of a class of non-weight modules and highest weight modules over the Virasoro algebra. We determine the necessary and sufficient conditions for such modules to be simple and the isomorphism classes among all these modules. Finally, we prove that these simple non-weight modules are new if the highest weight module over the Virasoro algebra is non-trivial.

scholarly journals Duflo theorem for a class of generalized Weyl algebras

2015 ◽  
Vol 14 (10) ◽  
pp. 1550147 ◽  
Author(s):  
Joanna Meinel
Keyword(s):  
Special Class ◽  
Simple Module ◽  
Weight Module ◽  
Highest Weight Module ◽  
Weyl Algebras ◽  
Highest Weight ◽  
Generalized Weyl Algebras

For a special class of generalized Weyl algebras (GWAs), we prove a Duflo theorem stating that the annihilator of any simple module is in fact the annihilator of a simple highest weight module.

Quantum Groups: Singular Vectors and BGG Resolution

1992 ◽  
Vol 07 (supp01b) ◽  
pp. 623-643 ◽  
Author(s):  
Fyodor Malikov
Keyword(s):  
Quantum Group ◽  
Quantum Groups ◽  
Weight Module ◽  
Verma Modules ◽  
Highest Weight Module ◽  
Singular Vectors ◽  
Type Formula ◽  
Highest Weight ◽  
Finite Dimensional ◽  
Dimensional Module

We prove existence of BGG resolution of an irreducible highest weight module over a quantum group, classify morphisms of Verma modules over a quantum group and find formulas for singular vectors in Verma modules. As an application we find cohomology of the quantum group of the type [Formula: see text] with coefficients in a finite-dimensional module.

Quasi-finite Irreducible Graded Modules for the Virasoro-like Algebra

2013 ◽  
Vol 20 (02) ◽  
pp. 181-196 ◽  
Author(s):  
Weiqiang Lin ◽  
Yucai Su
Keyword(s):  
Weight Module ◽  
Highest Weight Module ◽  
Graded Modules ◽  
Highest Weight ◽  
Finite Dimensional ◽  
Irreducible Modules ◽  
Graded Module ◽  
Intermediate Series ◽  
Uniformly Bounded

In this paper, we consider the classification of irreducible Z- and Z2-graded modules with finite-dimensional homogeneous subspaces over the Virasoro-like algebra. We prove that such a module is a uniformly bounded module or a generalized highest weight module. Then we determine all generalized highest weight quasi-finite irreducible modules. As a consequence, we determine all the modules with nonzero center. Finally, we prove that there does not exist any non-trivial Z-graded module of intermediate series.

Modules for loop Affine-Virasoro algebras

2020 ◽  
pp. 2150055 ◽  
Author(s):  
S. Eswara Rao
Keyword(s):  
Central Element ◽  
Weight Module ◽  
Verma Modules ◽  
Triangular Decomposition ◽  
Necessary And Sufficient Condition ◽  
Highest Weight Module ◽  
Highest Weight ◽  
Finite Dimensional ◽  
Integrable Module ◽  
Necessary And Sufficient

In this paper, we study the representations of loop Affine-Virasoro algebras. As they have canonical triangular decomposition, we define Verma modules and their irreducible quotients. We give necessary and sufficient condition for a irreducible highest weight module to have finite dimensional weight spaces. We prove that an irreducible integrable module is either a highest weight module or a lowest weight module whenever the canonical central element acts non-trivially. At the end, we construct Affine central operators for each integer and they commute with the action of the Affine Lie algebra.

A commutant of βγ-system associated to the highest weight module V4 of sl(2,C)

2010 ◽  
Vol 51 (9) ◽  
pp. 092301 ◽  
Author(s):  
Yan-Jun Chu ◽  
Fang Huang ◽  
Zhu-Jun Zheng
Keyword(s):  
Weight Module ◽  
Highest Weight Module ◽  
Highest Weight

scholarly journals Combinatorial bases of modules for affine Lie algebra B 2(1)

2013 ◽  
Vol 11 (2) ◽  
Author(s):  
Mirko Primc
Keyword(s):  
Lie Algebra ◽  
Vertex Operator ◽  
Vertex Operator Algebra ◽  
Intertwining Operators ◽  
Type B ◽  
Highest Weight Module ◽  
Highest Weight ◽  
Affine Lie Algebra ◽  
Algebra Theory ◽  
Simple Currents

AbstractWe construct bases of standard (i.e. integrable highest weight) modules L(Λ) for affine Lie algebra of type B 2(1) consisting of semi-infinite monomials. The main technical ingredient is a construction of monomial bases for Feigin-Stoyanovsky type subspaces W(Λ) of L(Λ) by using simple currents and intertwining operators in vertex operator algebra theory. By coincidence W(kΛ0) for B 2(1) and the integrable highest weight module L(kΛ0) for A 1(1) have the same parametrization of combinatorial bases and the same presentation P/I.

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