In this paper we first prove the PBW theorem for reduced universal enveloping algebras of restricted Lie superalgebras. Then the notion of an induced module is introduced and the dimension formula of induced modules i...In this paper we first prove the PBW theorem for reduced universal enveloping algebras of restricted Lie superalgebras. Then the notion of an induced module is introduced and the dimension formula of induced modules is established. Finally, using the results above, we obtain a property of induced modules pertaining to automorphisms of Lie superalgebras and isomorphisms of modules.展开更多
In this paper,we construct certain irreducible infinite dimensional representations of algebraic groups with Frobenius maps.In particular,a few classical results of Steinberg and Deligne&Lusztig on complex represe...In this paper,we construct certain irreducible infinite dimensional representations of algebraic groups with Frobenius maps.In particular,a few classical results of Steinberg and Deligne&Lusztig on complex representations of finite groups of Lie type are extended to reductive algebraic groups with Frobenius maps.展开更多
We study the representations of code vertex operator superalgebras resulting from a binary linear code which contains codewords of odd weight. We also show that there exists only one set of seven mutually orthogonal c...We study the representations of code vertex operator superalgebras resulting from a binary linear code which contains codewords of odd weight. We also show that there exists only one set of seven mutually orthogonal conformal vectors with central charge 1/2 in the Hamming code vertex operator superalgebra MH7. Phrthermore, we classify all the irreducible weak MH7-modules.展开更多
A simpler description of the representations of the Witt algebra is given, which is based on establishing a reductive lemma of central characters under its automorphism group and a simpler criterion of the simplicity ...A simpler description of the representations of the Witt algebra is given, which is based on establishing a reductive lemma of central characters under its automorphism group and a simpler criterion of the simplicity of induced modules.展开更多
In this paper,we obiain a theorem for the classification of the irreducible Harich-Chandra modules over G,Where G is a basic classical Lie superalgebra of I type. And the list of the classificatication is given for G=...In this paper,we obiain a theorem for the classification of the irreducible Harich-Chandra modules over G,Where G is a basic classical Lie superalgebra of I type. And the list of the classificatication is given for G=A(1,0).展开更多
文摘In this paper we first prove the PBW theorem for reduced universal enveloping algebras of restricted Lie superalgebras. Then the notion of an induced module is introduced and the dimension formula of induced modules is established. Finally, using the results above, we obtain a property of induced modules pertaining to automorphisms of Lie superalgebras and isomorphisms of modules.
基金supported by National Natural Science Foundation of China (Grant No. 11321101)
文摘In this paper,we construct certain irreducible infinite dimensional representations of algebraic groups with Frobenius maps.In particular,a few classical results of Steinberg and Deligne&Lusztig on complex representations of finite groups of Lie type are extended to reductive algebraic groups with Frobenius maps.
文摘We study the representations of code vertex operator superalgebras resulting from a binary linear code which contains codewords of odd weight. We also show that there exists only one set of seven mutually orthogonal conformal vectors with central charge 1/2 in the Hamming code vertex operator superalgebra MH7. Phrthermore, we classify all the irreducible weak MH7-modules.
文摘A simpler description of the representations of the Witt algebra is given, which is based on establishing a reductive lemma of central characters under its automorphism group and a simpler criterion of the simplicity of induced modules.
文摘In this paper,we obiain a theorem for the classification of the irreducible Harich-Chandra modules over G,Where G is a basic classical Lie superalgebra of I type. And the list of the classificatication is given for G=A(1,0).
