The edge-of-wedge type embeddings of dereived functor modules for the type A classical groups

Homological degrees of representations of categories with shift functors

Let $k$ be a commutative Noetherian ring and $\underline{\mathscr{C}}$ be a locally finite $k$-linear category equipped with a self-embedding functor of degree 1. We show under a moderate condition that finitely generated torsion representations of $\underline{\mathscr{C}}$ are super finitely presented (that is, they have projective resolutions each term of which is finitely generated). In the situation that these self-embedding functors are genetic functors, we give upper bounds for homological degrees of finitely generated torsion modules. These results apply to quite a few categories recent…

Asymptotic Schur decomposition of Veronese syzygy functors

The syzygies of the d-th Veronese embedding of $\mathbb P(V)$ are functors of the complex vector space V. From a certain perspective, we show that as d grows, their Schur functor decomposition is very rich whenever they are not zero. This is deduced from an asymptotic study of related plethysms. We also obtain other results related to a question of Ein and Lazarsfeld.

缺陷、Malgrange函子与线性控制系统

The defect, the Malgrange functor, and linear control systems

本文将有限表示函子的缺陷概念推广至任意加性函子，证明其与反变Yoneda嵌入构成右伴随对，并揭示模投射元的共变Hom缺陷等同于Bass挠，进而应用于线性控制系统得出Malgrange函子缺陷与系统自治性同构的结论。

顶点算子代数的有限诱导函子

Finite induction functor for vertex operator algebras

本文为顶点算子代数的嵌入引入有限诱导函子，证明其满足 Frobenius 互反律等性质，并明确计算了标准子代数和抛物型子代数上不可约模的有限诱导。

由顺序嵌入定义的持续模块不变量

Invariants of persistence modules defined by order-embeddings

本文研究了通过顺序嵌入获得的持续模块不变量，探讨了通过分解给定模块到子持续集的限制来获得不变量的方法，并通过同调学视角重新解释了先前结果。

Generalised Moore spectra in a triangulated category

In this paper we consider a construction in an arbitrary triangulated category T which resembles the notion of a Moore spectrum in algebraic topology. Namely, given a compact object C of T satisfying some finite tilting assumptions, we obtain a functor which "approximates" objects of the module category of the endomorphism algebra of C in T. This generalises and extends a construction of Jorgensen in connection with lifts of certain homological functors of derived categories. We show that this new functor is well-behaved with respect to short exact sequences and distinguished triangles, and as…

Embedding Deligne's category $\mathrm{\underline{Re}p}(S_t)$ in the Heisenberg category

We define a faithful linear monoidal functor from the partition category, and hence from Deligne's category $\mathrm{\underline{Re}p}(S_t)$, to the Heisenberg category. We show that the induced map on Grothendieck rings is injective and corresponds to the Kronecker coproduct on symmetric functions.

Rational and trigonometric degeneration of the double affine Hecke algebra of type $A$

We study a connection between the representation theory of the rational Cherednik algebra of type $GL_n$ and the representation theory of the degenerate double affine Hecke algebra (the degenerate DAHA). We focus on an algebra embedding from the rational Cherednik algebra to the degenerate DAHA and investigate the induction functor through this embedding. We prove that this functor embeds the category ${\mathcal O}$ for the rational Cherednik algebra fully faithfully into the category ${\mathcal O}$ for the degenerate DAHA. We also study the full subcategory ${\mathcal O}^{ss}$ of ${\mathcal O…

Cherednik代数上完整模的回拉和推出函子

Pull-back and push-forward functors for holonomic modules over Cherednik algebras

本文在Cherednik代数层上，通过建立b-函数理论证明开嵌入和闭嵌入下完整性的保持，进而证明任意拟态射下推出和回拉保持完整性，并给出不可约完整模的分类及Ext-群的有限维性。

Tilting modules of affine quasi-hereditary algebras

We discuss tilting modules of affine quasi-hereditary algebras. We present an existence theorem of indecomposable tilting modules when the algebra has a large center and use it to deduce a criterion for an exact functor between two affine highest weight categories to give an equivalence. As an application, we prove that the Arakawa-Suzuki functor [Arakawa-Suzuki, J. of Alg. 209 (1998)] gives a fully faithful embedding of a block of the deformed BGG category of $\mathfrak{gl}_{m}$ into the module category of a suitable completion of degenerate affine Hecke algebra of $GL_{n}$.