相关论文: On the simplicity of Kac modules for the restricte…
In this paper, we study the simple modules for the restricted Lie superalgebra $gl(m|n)$. A condition for the simplicity of the induced modules is given, and an analogue of Kac-Weisfeiler theorem is proved.
The simplicity of the Kac modules for the quantum superalgebra U_q(gl(m,n)) is studied, and the relation between the representation of U_q(gl(m,n)) and that of U_q(g_{\0}) is investigated.
Simple modules for the restricted Witt superalgebra $W(m,n,1)$ are considered. Conditions are provided for the restricted and nonrestricted Kac modules to be simple.
Let $\mathfrak{g}=\mathfrak{g}_{\bar{0}}\oplus \mathfrak{g}_{\bar{1}}$ be a classical Lie superalgebra and $\mathcal{F}$ be the category of finite dimensional $\mathfrak{g}$-supermodules which are completely reducible over the reductive Lie…
This paper aims to describe the restricted Kac modules of restricted Hamiltonian Lie superalgebras of odd type over an algebraically closed field of characteristic $p>3$. In particular, a sufficient and necessary condition for the…
The problem of computing the characters of the finite dimensional irreducible representations of the Lie superalgebra $\mathfrak{gl}(m|n)$ over $\C$ was solved a few years ago by V. Serganova. In this article, we present an entirely…
The multiplicities a_{lambda,mu} of simple modules L(mu) in the composition series of Kac modules V(lambda) for the Lie superalgebra gl(m/n) were described by Serganova, leading to her solution of the character problem for gl(m/n). In…
The complexity of the simple and the Kac modules over the general linear Lie superalgebra $\mathfrak{gl}(m|n)$ of type $A$ was computed by Boe, Kujawa, and Nakano in 2012. A natural continuation to their work is computing the complexity of…
Character formulas for Lie superalgebras have been shown to have important applications to number theory and combinatorics. We prove the Kac-Wakimoto character formula for the general linear Lie superalgebra gl(m|n). This formula…
Let $\frak{g}$ be a contact Lie superalgebra of odd type or special contact Lie superalgebra of odd type over an algebraically closed field of characteristic $p>3$. In this paper we study non-restricted representations of $\frak{g}$. By…
The composition factors of Kac-modules for the general linear Lie superalgebras $gl_{m|n}$ are explicitly determined. In particular, a conjecture of Hughes, King and van der Jeugt in [J. Math. Phys., 41 (2000), 5064-5087] is proved.
The simplicity of the induced modules for reductive Lie algebras over an algebraically closed field of positive characteristic is studied, and a necessary and sufficient condition for the simplicity is given.
The generalized p-characters for the restricted Lie color are defined. The simplicity of the induced modules for the FP triples are determined. As applications, we have obtained an analogue of the Kac-Weisfiler theorem for the algebraic Lie…
We show that, for many Lie superalgebras admitting a compatible $\mathbb{Z}$-grading, Kac induction functor gives rise to a bijection between simple supermodules over a Lie superalgebra and simple supermodules over the even part of this Lie…
For a restricted Lie superalgebra g over an algebraically closed field of characteristic p > 2, we generalize the deformation method of Premet and Skryabin to obtain results on the p-power and 2-power divisibility of dimensions of…
Let $H(2,1;\underline{t})$ be Hamiltonian superalgebras over $\mathbb{F}$, an algebraically closed field of prime characteristic $p>3$, which are non-restricted simple Lie superalgebras, generally. In this paper, we study generalized…
In this paper, the correspondence between the finite dimensional representations of a simple Lie algebra and their characteristic polynomials is established, and a monoid structure on these characteristic polynomials is constructed.…
We first present a filtration on the ring L of Laurent polynomials such that the direct sum decomposition of its associated graded ring gr L agrees with the direct sum decomposition of gr L, as a module over the complex general linear Lie…
To study finite-dimensional modules of the Lie superalgebras, Kac introduced the Kac-modules and divided them into typical or atypical modules according as they are simple or not. For Lambda being atypical, Hughes et al have an algorithm to…
The generalized Kazhdan-Lusztig polynomials for the finite dimensional irreducible representations of the general linear superalgebra are computed explicitly. Using the result we establish a one to one correspondence between the set of…