6 problems

Let $X$ be a quantum supermatrix with even dimension $m$ and odd dimension $n$. Let $\e_i(\omega_1,\ldots,\omega_m)$ and $e_j(\varpi_1,\ldots,\varpi_n)$ denote the elementary symme…

Let $X$ be a quantum supermatrix, let $m$ and $n$ denote its even and odd dimensions, and let the quantum super analog of Littlewood correspondence III refer to the expression of S…

Let $E=\varepsilon_{0}\oplus\varepsilon_{1}$ be an arbitrary $\mathbb{Z}_{2}$-grading on the Grassmann algebra, and let $L$ be its underlying vector space. Homogeneous-generator co…

Let $L$ be the vector space underlying the Grassmann algebra $E$, and let $E=\varepsilon_{0}\oplus\varepsilon_{1}$ be a $\mathbb{Z}_{2}$-grading. A basis of $L$ is called adapted t…

Equivalence conjecture. The $SL(2,\mathbb{Z})$ representation defined by the handle-algebra transformations on $\mathfrak{R}_{(\mathcal{A})}\cong Z(\mathcal{G})$ and the Lyubashenk…

Let $\Lambda$ be a superpartition with $m$ circles, and let $\Lambda^*$ and $\Lambda^\circledast$ denote the associated ordinary partitions. For a scalar product…