论文标题
量子酷超级组通过V-差异操作员
Quantum queer supergroups via v-differential operators
论文作者
论文摘要
通过使用某些量子差分运算符，我们为量子酷超级组U_V（q_n）构建了一个超级表示。该表示形式的基本空间是2n^2变量中的变形多项式超级，其同质组件可以用作Quer Q-Schur Superalgebras的基础空间。然后，我们将表示形式扩展到其正式的功率系列代数，该代数包含（超级）supperule同构与U_V（q_n）的常规表示形式。 U_V（Q_N）的单一基础M在证明同构中起关键作用。通过这种方式，我们可以通过另一个新基础L以及生成器的某些显式乘法公式来呈现量子Queer SuperGroup U_V（Q_N）。作为应用程序，通过上述均匀组件获得了Queer Q-Schur Superalgebras的类似演示。 基地M和L的存在以及新的演讲表明，贝利森·卢斯蒂格·麦克弗森（Beilinson-Lusztig-Macpherson）建立的量子GL_N的开创性构建30年前通过完全不同的方法扩展到了这种“酷儿”量子超级组。
By using certain quantum differential operators, we construct a super representation for the quantum queer supergroup U_v(q_n). The underlying space of this representation is a deformed polynomial superalgebra in 2n^2 variables whose homogeneous components can be used as the underlying spaces of queer q-Schur superalgebras. We then extend the representation to its formal power series algebra which contains a (super) submodule isomorphic to the regular representation of U_v(q_n). A monomial basis M for U_v(q_n) plays a key role in proving the isomorphism. In this way, we may present the quantum queer supergroup U_v(q_n) by another new basis L together with some explicit multiplication formulas by the generators. As an application, similar presentations are obtained for queer q-Schur superalgebras via the above mentioned homogeneous components. The existence of the bases M and L and the new presentation show that the seminal construction of quantum gl_n established by Beilinson-Lusztig-MacPherson thirty years ago extends to this "queer" quantum supergroup via a completely different approach.
