论文标题
使用有限尺寸超级甲壳（初步版本）接近量子酷儿超组
Approaching quantum queer supergroups using finite dimensional superalgebras (Preliminary version)
论文作者
论文摘要
Beilinson-Lusztig-Macpherson [blm]首先引入了使用有限维代数来接近量子线性组的序列（即，量子$ \ mathfrak {gl} _n $）的想法。在他们的工作中，代数是某些有限的部分旗品品种的卷积代数，其某些结构相对于轨道基础具有满足稳定特性。该属性导致无限尺寸的代数的定义。最后，进行限制过程会产生量子$ \ mathfrak {gl} _n $的新实现。从那时起，这项工作已进行了修改[DF2]，并将其概括为量子，$ \ Mathfrak {gl} _n $（有关几何方法，请参见[GV，L]，以及[DDF，DF]的代数方法和新的实现方法和新的实现）和量子super $ \ mathfrak {Glfrak {gl} _ _ n} $ [dg]从类型$ b/c $几何形状和$ i $ -Quantum组$ \ boldsymbol u^\ jmath $和$ \ boldsymbol u^\ imath $;参见[BKLW，DWU1，DWU2]。本文通过有限的尺寸酷儿$ q $ -schur superalgebras扩展了量子酷儿超级组$ u_ {v}（\ mathfrak {q} _n）$的代数方法。
The idea of using a sequence of finite dimensional algebras to approach a quantum linear group (i.e., a quantum $\mathfrak{gl}_n$) was first introduced by Beilinson-Lusztig-MacPherson [BLM]. In their work, the algebras are convolution algebras of some finite partial flag varieties whose certain structure constants relative to the orbital basis satisfy a stabilization property. This property leads to the definition of an infinite dimensional idempotented algebra. Finally, taking a limit process yields a new realization for the quantum $\mathfrak{gl}_n$. Since then, this work has been modified [DF2] and generalized to quantum affine $\mathfrak{gl}_n$ (see [GV, L] for the geometric approach and [DDF, DF] for the algebraic approach and a new realization) and quantum super $\mathfrak{gl}_{m|n}$ [DG], and, more recently, to convolution algebras arising from type $B/C$ geometry and $i$-quantum groups $\boldsymbol U^\jmath$ and $\boldsymbol U^\imath$; see [BKLW, DWu1, DWu2]. This paper extends the algebraic approach to the quantum queer supergroup $U_{v}(\mathfrak{q}_n)$ via finite dimensional queer $q$-Schur superalgebras.
