All Questions

Let $\chi_{\mu}^{\lambda}$ denote a value of an irreducible character of the symmetric group $\frak{S}_n$, where $\mu, \lambda\vdash n$. When $\mu=(n)$, then it's known that $$\sum_{\lambda\vdash n}\...

Let $s_{\lambda}$ denote the Schur polynomial associated to a partition $\lambda$. A partition $\lambda$ is called a $t$-core if none of its hook lengths are multiples of $t$. QUESTION. Consider the ...

Given a partition $\lambda$, the Schur polynomials can be defined, among many other ways, as $$S_{\lambda}(\xi_1,\dots,\xi_a)=\frac{\det\left(\xi_i^{\lambda_j+a-j}\right)_{i,j=1}^a}{\det\left(\xi_i^{a-...