Related papers: A superdimension formula for gl(m|n) modules

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…

We prove the Kac-Wakimoto conjecture for the periplectic Lie superalgebra $\mathfrak{p}(n)$, stating that any simple module lying in a block of non-maximal atypicality has superdimension zero.

In this paper, we study the representations of the periplectic Lie superalgebra using the Duflo-Serganova functor. Given a simple $\mathfrak{p}(n)$-module $L$ and a certain element $x\in \mathfrak{p}(n)$ of rank $1$, we give an explicit…

Suppose $g=g_0+g_1$ is a finite-dimensional restricted Lie superalgebra over an algebraically closed field $k$ of characteristic $p>2$. In this article, we propose a conjecture for maximal dimensions of irreducible modules over the…

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 $\ggg:=\gl_{m|n}$ be a general linear Lie superalgebra over an algebraically closed field $\mathds{k}=\overline{\mathbb{F}}_p$ of characteristic $p>2$. A module of $\ggg$ is said to be of Kac-Weisfeiler if its dimension coincides with…

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…

In 1994, Kac and Wakimoto suggested a generalization of Bernstein and Leites character formula for basic Lie superalgebras, and the natural question was raised: to which simple highest weight modules does it apply? In this paper, we prove a…

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…

We establish an explicit formula for the character of an irreducible finite-dimensional representation of $\mathfrak{gl}(m|n)$. The formula is a finite sum with integer coefficients in terms of a basis $\mathcal{E}_{\mu}$ (Euler characters)…

In this paper we formulate a conjecture about the minimal dimensional representations of the finite $W$-superalgebra $U(\mathfrak{g}_\bbc,e)$ over the field of complex numbers and demonstrate it with examples including all the cases of type…

Let $\mathfrak g=\mathfrak g_{\bar 0}\oplus\mathfrak g_{\bar 1}$ be the queer Lie superalgebra and let $L$ be a finite-dimensional non-trivial irreducible $\mathfrak g$-module. Restricting the $\mathfrak g$-action on $L$ to $\mathfrak…

In this paper we give a new formula for characters of finite dimensional irreducible $\frak{gl}(m,n)$ modules. We use two main ingredients: Su-Zhang formula and Brion's theorem.

We consider the finite W-superalgebras for a basic classical Lie superalgebra g associated with an even nilpotent element in g both over the field of complex numbers field and and over a filed of positive characteristic. We present the PBW…

In this paper we construct resolutions of finite dimensional irreducible gl(m|n)-modules in terms of generalized Verma modules. The resolutions are determined by the Kostant cohomology groups and extend the strong…

Methods are developed for systematically constructing the finite dimensional irreducible representations of the super Yangian Y(gl(M|N)) associated with the Lie superalgebra gl(M|N). It is also shown that every finite dimensional…

We develop a new method to solve the irreducible character problem for a wide class of modules over the general linear superalgebra, including all the finite-dimensional modules, by directly relating the problem to the classical…

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.

In this paper, we used the free fields of Wakimoto to construct a class of irreducible representations for the general linear Lie superalgebra $\mathfrak{gl}_{m|n}(\mathbb{C})$. The structures of the representations over the general linear…

Atypicality is a fundamental combinatorial invariant for simple supermodules of a basic Lie superalgebra. Boe, Nakano, and the author gave a conjectural geometric interpretation of atypicality via support varieties. Inspired by low…