Duflo-Serganova函子，二十年之后

Grothendieck rings for Lie superalgebras and the Duflo-Serganova functor

We show that the Duflo-Serganova functor on the category of finite-dimensional modules over a finite-dimensional contragredient Lie superalgebra induces a ring homomorphism on a natural quotient of the Grothendieck ring, which is isomorphic to the ring of characters. We realize this homomorphism as a certain evaluation of functions related to the supersymmetry property. We use this realization to describe the kernel and image of the homomorphism induced by the Duflo-Serganova functor.

Gruson-Serganova character formulas and the Duflo-Serganova cohomology functor

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 $\mathcal{E}_μ$ (Euler characters) of the character ring. We prove a simple formula for the behaviour of the ``superversion'' of $\mathcal{E}_μ$ in the $\mathfrak{gl}(m|n)$ and $\mathfrak{osp}(m|2n)$-case under the map $ds$ on the supercharacter ring induced by the Duflo-Serganova cohomology functor $DS$. As an application we get combinatorial formulas for superdimensions, dimensions and $\mathf…

论 Duflo-Serganova 函子的对称性

On symmetries of the Duflo-Serganova functor

本文研究 Duflo-Serganova 函子的对称性，构造作用于其上的 Lie 超代数、Lie 超群与结合超代数，并把 GL(n|n) 的 Kac 模相关结果推广至 P(n)。

On the Duflo-Serganova functor for the queer Lie superalgebra

We study the Duflo-Serganova functor $\operatorname{DS}_x$ for the queer Lie superalgebra $\mathfrak{q}_n$ and for all odd $x$ with $[x,x]$ semisimple. For the case when the rank of $x$ is $1$ we give a formula for multiplicities in terms of the arc diagram attached to $λ$. Further, we prove that $\operatorname{DS}_x(L)$ is semisimple if $L$ is a simple finite-dimensional module and $x$ is of rank $1$ satisfying $x^2=0$.

正特征下Duflo-Serganova函子的注记

Notes on the Duflo-Serganova functor in positive characteristic

本文在奇特征域下研究Duflo-Serganova函子，拓展了对称超群的计算方法并应用于典型超群情形，还证明了拟约化超群上超模内射性的判据，推进了正特征下该函子的理论研究。

Duflo-Serganova functor and superdimension formula for the periplectic Lie superalgebra

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 description of the composition factors of the $\mathfrak{p}(n-1)$-module $DS_x(L)$, which is defined as the homology of the complex $$ΠM \xrightarrow{x} M \xrightarrow{x} ΠM.$$ In particular, we show that this $\mathfrak{p}(n-1)$-module is multiplicity-free. We then use this result to give a simple explicit combinatorial formula for the superdimension of a simp…