On the representations of Sp(p,q) and SO^\ast(2n) unitarily induced from derived functor modules

On the categorical entropy of the Frobenius pushforward functor

In this paper, we consider the Frobenius pushforward endofunctor $F_\ast$ of the bounded derived category of finitely generated modules over an $F$-finite noetherian local ring. We completely determine the categorical entropy of $F_\ast$ in the sense of Dimitrov, Haiden, Katzarkov, and Kontsevich.

Staggered and affine Kac modules over $A_1^{(1)}$

This work concerns the representation theory of the affine Lie algebra $A_1^{(1)}$ at fractional level and its links to the representation theory of the Virasoro algebra. We introduce affine Kac modules as certain finitely generated submodules of Wakimoto modules. We conjecture the existence of several classes of staggered $A_1^{(1)}$-modules and provide evidence in the form of detailed examples. We extend the applicability of the Goddard-Kent-Olive coset construction to include the affine Kac and staggered modules. We introduce an exact functor between the associated category of $A_1^{(1)}$-m…

Γ-graded 一般线性李 ω-代数的不变量与表示

Invariants and representations of the $Γ$-graded general linear Lie $ω$-algebras

本文研究了Γ-graded一般线性李ω-代数的表示论与不变量理论，建立了广义Howe对偶性，推导了不变量理论的基本定理和广义Schur-Weyl对偶性，并分析了单位化模的分类及Hopf(Γ,ω)-代数的构造。