论文标题
关于Quiver Grassmannians for ocyclic箭
On the cohomology of quiver Grassmannians for acyclic quivers
论文作者
论文摘要
对于无环颤抖，我们建立了Quiver grassmannians的共同体与代数$ u_q^ - （\ Mathfrak {g}）$的双重规范基础之间的联系，其中$ u_q^ - （\ m mathfrak {g}）$是与Quiverbra相关的量化量子的负面的一半。为了实现这一目标，我们通过Lusztig的类别研究了Quiver Grassmannians的同谋。结果，我们从双重规范基础的系数方面明确描述了刚性颤抖的司羊glas骨的多项式，这被视为量子散装代数的要素。通过这个结果，我们给出了另一个证据，证明了奇异的Quiver Grassmanians奇怪的同种学的定理。同时，对于dynkin颤抖，我们表明，刚性箭袋的圆盘多项式是代数$ u_q^ - （\ Mathfrak {g}）$的双PBW基础的系数。
For an acyclic quiver, we establish a connection between the cohomology of quiver Grassmannians and the dual canonical bases of the algebra $U_q^-(\mathfrak{g})$, where $U_q^-(\mathfrak{g})$ is the negative half of the quantized enveloping algebra associated with the quiver. In order to achieve this goal, we study the cohomology of quiver Grassmannians by Lusztig's category. As a consequence, we describe explicitly the Poincaré polynomials of rigid quiver Grassmannians in terms of the coefficients of dual canonical bases, which are viewed as elements of quantum shuffle algebras. By this result, we give another proof of the odd cohomology vanishing theorem for quiver Grassmanians. Meanwhile, for Dynkin quivers, we show that the Poincaré polynomials of rigid quiver Grassmannians are the coefficients of dual PBW bases of the algebra $U_q^-(\mathfrak{g})$.
