Maximaland Primitive Elements in Baby Verma Modules for Type $B_2$

增强 nilHecke 代数与 baby Verma 模

Enhanced nilHecke algebras and baby Verma modules

本文通过在增强 nilHecke 代数上构造导子得到 p-dg 代数，并利用 p-dg 模范畴上的函子在 Grothendieck 群上实现小量子 sl2 作用，进而将其提升为李代数 sl(2) 的作用，揭示其与 baby Verma 模的同构关系。

Verma Modules for Restricted Quantum Groups at a Fourth Root of Unity

For a semisimple Lie algebra $\mathfrak{g}$ of rank $n$, let $\overline{U}_ζ(\mathfrak{g})$ be the restricted quantum group of $\mathfrak{g}$ at a primitive fourth root of unity. This quantum group admits a natural Borel-induced representation $V({\boldsymbol{t}})$, with ${\boldsymbol{t}}\in(\mathbb{C}^\times)^n$ determined by a character on the Cartan subalgebra. Ohtsuki showed that for $\mathfrak{g}=\mathfrak{sl}_2$, the braid group representation determined by tensor powers of $V({\boldsymbol{t}})$ is the exterior algebra of the Burau representation. In this paper, we generalize the tensor …

Singular dimensions of the N=2 superconformal algebras II: the twisted N=2 algebra

We introduce a suitable adapted ordering for the twisted N=2 superconformal algebra (i.e. with mixed boundary conditions for the fermionic fields). We show that the ordering kernels for complete Verma modules have two elements and the ordering kernels for G-closed Verma modules just one. Therefore, spaces of singular vectors may be two-dimensional for complete Verma modules whilst for G-closed Verma modules they can only be one-dimensional. We give all singular vectors for the levels 1/2, 1, and 3/2 for both complete Verma modules and G-closed Verma modules. We also give explicit examples of d…