In this paper,we construct a superfermionic representation as well as a vertex representation for twisted general linear affine Lie superalgebras.We also establish a module isomorphism between them,which generalizes t...In this paper,we construct a superfermionic representation as well as a vertex representation for twisted general linear affine Lie superalgebras.We also establish a module isomorphism between them,which generalizes the super boson-fermion correspondence of type B given by Kac-van de Leur.Based on this isomorphism,we determine explicitly the irreducible components of these two representations.Particularly,we obtain in this way two kinds of systematic construction of level 1 irreducible integrable highest weight modules for twisted general linear affine Lie superalgebras.展开更多
During the last decade, a great deal of activity has been devoted to the calculation of the HilbertPoincar′e series of unitary highest weight representations and related modules in algebraic geometry. However,uniform...During the last decade, a great deal of activity has been devoted to the calculation of the HilbertPoincar′e series of unitary highest weight representations and related modules in algebraic geometry. However,uniform formulas remain elusive—even for more basic invariants such as the Gelfand-Kirillov dimension or the Bernstein degree, and are usually limited to families of representations in a dual pair setting. We use earlier work by Joseph to provide an elementary and intrinsic proof of a uniform formula for the Gelfand-Kirillov dimension of an arbitrary unitary highest weight module in terms of its highest weight. The formula generalizes a result of Enright and Willenbring(in the dual pair setting) and is inspired by Wang's formula for the dimension of a minimal nilpotent orbit.展开更多
The authors prove the stability of the rings of highest weight vectors of the action of Om x GLn on the complex polynomial rings on Cm,n. As an application, the structure of the rings for m = 3 is determined.
We investigate the highest weight representations of the q-deformed Virasoro algebra of Hom-type. In order to determine its unitarity and irreducible highest weight representations, we present its Kac determinant form...We investigate the highest weight representations of the q-deformed Virasoro algebra of Hom-type. In order to determine its unitarity and irreducible highest weight representations, we present its Kac determinant formula when q is nonzero and non-root of unity.展开更多
The simple modules for electrical Lie algebra of type D5 were investigated.The sufficient and necessary criteria of the simple Z-graded highest weight modules were established by means of determining the singular vect...The simple modules for electrical Lie algebra of type D5 were investigated.The sufficient and necessary criteria of the simple Z-graded highest weight modules were established by means of determining the singular vectors of the Verma modules.The simple highest weight module is isomorphic to either that for the symplectic Lie algebra sp4 or Verma module.展开更多
基金supported by National Natural Science Foundation of China(Grant No.12161141001)the Fundamental Research Funds for the Central Universities(Grant No.20720230020)S.Tan is supported by National Natural Science Foundation of China(Grant No.12131018)。
文摘In this paper,we construct a superfermionic representation as well as a vertex representation for twisted general linear affine Lie superalgebras.We also establish a module isomorphism between them,which generalizes the super boson-fermion correspondence of type B given by Kac-van de Leur.Based on this isomorphism,we determine explicitly the irreducible components of these two representations.Particularly,we obtain in this way two kinds of systematic construction of level 1 irreducible integrable highest weight modules for twisted general linear affine Lie superalgebras.
基金supported by National Natural Science Foundation of China(Grant No.11171324)the Hong Kong Research Grants Council under RGC Project(Grant No.60311)the Hong Kong University of Science and Technology under DAG S09/10.SC02.
文摘During the last decade, a great deal of activity has been devoted to the calculation of the HilbertPoincar′e series of unitary highest weight representations and related modules in algebraic geometry. However,uniform formulas remain elusive—even for more basic invariants such as the Gelfand-Kirillov dimension or the Bernstein degree, and are usually limited to families of representations in a dual pair setting. We use earlier work by Joseph to provide an elementary and intrinsic proof of a uniform formula for the Gelfand-Kirillov dimension of an arbitrary unitary highest weight module in terms of its highest weight. The formula generalizes a result of Enright and Willenbring(in the dual pair setting) and is inspired by Wang's formula for the dimension of a minimal nilpotent orbit.
基金Project supported by the National Natural Science Foundation of China (No.19901015 and No. 19731004).
文摘The authors prove the stability of the rings of highest weight vectors of the action of Om x GLn on the complex polynomial rings on Cm,n. As an application, the structure of the rings for m = 3 is determined.
基金Supported by the National Natural Science Foundation of China(11047030)Supported by the Science and Technology Program of Henan Province(152300410061)
文摘We investigate the highest weight representations of the q-deformed Virasoro algebra of Hom-type. In order to determine its unitarity and irreducible highest weight representations, we present its Kac determinant formula when q is nonzero and non-root of unity.
基金Fundamental Research Funds for the Central Universities,China(No.2232021G13)。
文摘The simple modules for electrical Lie algebra of type D5 were investigated.The sufficient and necessary criteria of the simple Z-graded highest weight modules were established by means of determining the singular vectors of the Verma modules.The simple highest weight module is isomorphic to either that for the symplectic Lie algebra sp4 or Verma module.
