NilCoxeter algebras categorify the Weyl algebra

Frobenius扩张与$G(m,m,3)$的奇异 nilCoxeter 代数

Frobenius extensions and the exotic nilCoxeter algebra for $G(m,m,3)$

本文引入了q-形变除差算子，在复反射群$G(m,m,n)$下生成了奇异 nilCoxeter 代数，证明了新的迂回关系，并在$G(m,m,3)$的奇异 nilCoxeter 代数中识别了Frobenius迹。

Towers of graded superalgebras categorify the twisted Heisenberg double

We show that the Grothendieck groups of the categories of finitely-generated graded supermodules and finitely-generated projective graded supermodules over a tower of graded superalgebras satisfying certain natural conditions give rise to twisted Hopf algebras that are twisted dual. Then, using induction and restriction functors coming from such towers, we obtain a categorification of the twisted Heisenberg double and its Fock space representation. We show that towers of wreath product algebras (in particular, the tower of Sergeev superalgebras) and the tower of nilcoxeter graded superalgebras…

Polynomial functors and categorifications of Fock space II

We categorify various Fock space representations on the algebra of symmetric functions via the category of polynomial functors. In a prequel, we used polynomial functors to categorify the Fock space representations of type A affine Lie algebras. In the current work we continue the study of polynomial functors from the point of view of higher representation theory. Firstly, we categorify the Fock space representation of the Heisenberg algebra on the category of polynomial functors. Secondly, we construct commuting actions of the affine Lie algebra and the level p action of the Heisenberg algebr…

量子 $ε$ 电Hopf代数与Fock空间范畴化

The quantum $ε$lectrical Hopf algebra and categorification of Fock space

本文引入电KLR代数，证明其范畴化类型A电Lie代数的量子版本，并利用其循环商范畴化更高层Fock空间。

p-DG 分圆 nilHecke 代数

p-DG cyclotomic nilHecke algebras

本文通过 p-DG 分圆 nilHecke 代数，对量子 sl(2) 在素单位根处的两个 Weyl 模的张量积进行范畴化。

p-DG 分圆 nilHecke 代数 II

p-DG cyclotomic nilHecke algebras II

本文在早期范畴化两个 Weyl 模张量积的工作基础上，进一步对量子 $\mathfrak{sl}_2$ 在素单位根处的基本表示的张量积进行了范畴化。