q-Analogue of $A_{m-1}\oplus A_{n-1}\subset A_{mn-1}$

量子 queer 超代数的辫张量积与多项式不变量

Braided tensor products and polynomial invariants for the quantum queer superalgebra

本文构造量子奇异李超代数的超对称代数量子类似物，利用显式辫算子定义辫张量积并证明相关同构，最终得到其不变量的一组生成元。

Combinatorial bases of Feigin-Stoyanovsky's type subspaces of level 1 standard modules for $\tilde{\mathfrak sl}(\ell+1,\C)$

Let $\tilde{\mathfrak g}$ be an affine Lie algebra of type $A_\ell^{(1)}$. Suppose we're given a $\mathbb Z$-gradation of the corresponding simple finite-dimensional Lie algebra ${\mathfrak g}={\mathfrak g}_{-1}\oplus{\mathfrak g}_0 \oplus {\mathfrak g}_1$; then we also have the induced $\mathbb Z$-gradation of the affine Lie algebra $$\tilde{\mathfrak g}=\tilde{\mathfrak g}_{-1} \oplus \tilde{\mathfrak g}_0 \oplus \tilde{\mathfrak g}_1.$$ Let $L(Λ)$ be a standard module of level 1. Feigin-Stoyanovsky's type subspace $W(Λ)$ is the $\tilde{\mathfrak g}_1$-submodule of $L(Λ)$ generated by the hi…

Quantum isometries, noncommutative spheres, and related integrals

The sphere $S^{N-1}_\mathbb R$ has a half-liberated analogue $S^{N-1}_{\mathbb R,*}$, and a free analogue $S^{N-1}_{\mathbb R,+}$. This is a presentation of the construction and main properties of these noncommutative spheres, $S^{N-1}_\mathbb R\subset S^{N-1}_{\mathbb R,*}\subset S^{N-1}_{\mathbb R,+}$, and of their quantum isometry groups.